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President Biden and China’s leader, Xi Jinping, pledged at a virtual summit to improve cooperation, but offered no breakthroughs after three and a half hours of talks.

In separate statements after the talks ended, each side emphasized the points of contention that mattered most: lists of mutual grievances that underscored the depth of the divisions between them.

Mr. Biden, the White House said, raised concerns about human rights abuses and China’s “unfair trade and economic policies.” Mr. Xi said that American support for Taiwan was “playing with fire,” and warned that dividing the world into alliances or blocs — a pillar of the new administration’s strategy for challenging China by teaming up with its neighbors — would “inevitably bring disaster to the world.”

In advance of the meeting, White House officials had signaled that there would be no concrete agreements or initiatives, or even an effort to put out a joint statement — usually a pre-negotiated statement on areas of agreement or projects to tackle together.

The two leaders nevertheless expressed a willingness to manage their differences in a way that avoided conflict between the world’s two largest powers. That alone could lower temperature of a relationship that has at times this year threatened to overheat.

“It seems to me we need to establish some common-sense guardrails,” Mr. Biden said, using a phrase his administration has often cited as a goal for a challenging relationship. Addressing Mr. Xi directly, he added: “We have a responsibility to the world, as well as to our people.”

Although the two leaders have spoken by telephone twice this year, the conference was intended to replicate the more thorough discussion of issues of previous summits between the United States and China — something that was not possible because health and political concerns have kept Mr. Xi from traveling since January 2020.

Both men were accompanied by a phalanx of senior aides — the Americans in the Roosevelt Room at the White House and the Chinese inside a chamber in the Great Hall of the People in Beijing. In brief remarks at the beginning of the meeting, each struck a conciliatory tone, flagging areas of disagreement but also pledging to work together.

Mr. Biden, seated before two large screens, noted that the two have “spent an awful lot of time talking to each other” over the years, dating to when Mr. Biden was vice president and Mr. Xi was a rising power in the Chinese leadership. Mr. Xi said he was prepared to move relations “in a positive direction.”

“Although it’s not as good as a face-to-face meeting, I’m very happy to see my old friend,” Mr. Xi said.

Mr. Biden emphasized the need to keep “communication lines open,” according to a White House statement, as the two countries confront disagreements over issues like the future of Taiwan, the militarization of the South China Sea and China’s exploitation of vulnerabilities to bore deeply into the computer networks of American companies, especially defense contractors.

The call, which was initiated at Mr. Biden’s request, reflected his administration’s deep concern that the chances of keeping conflict at bay may be diminishing. Mr. Biden has repeatedly suggested that it should be possible to avoid active military engagement with China, even as the United States engages in vigorous competition with Beijing and continues to confront the Chinese leadership on several significant issues.

The statements hinted at some discussion of “strategic” issues, a phrase that appeared to encompass the nuclear strategies of both nations, but American officials declined to detail those discussions. Some issues that had been the source of speculation before the summit did not come up, including disputes over visas and an invitation to attend the Winter Olympics in Beijing, which begin in February.

Reporting and research by Steven Lee Myers, David E. Sanger, Claire Fu and Li You.

China’s leader, Xi Jinping, urged the United States not to test his country’s resolve on the question of Taiwan, an island democracy Beijing claims is part of its territory.

“We are patient and are willing to strive for the prospect of peaceful reunification with the utmost sincerity,” Mr. Xi told President Biden, according to a readout on the meeting released by Chinese state media. “But China will have to take resolute measures if the ‘Taiwan independence’ separatist forces provoke, compel or even cross the red line.”

In vivid language that has come to define Beijing’s strident rhetoric, Mr. Xi criticized politicians in the United States who he said sought to use the island’s status as leverage over Beijing — a trend he described as dangerous. “It is playing with fire, and if you play with fire, you will get burned,” the Chinese readout cited Mr. Xi as saying.

No issue between the United States and China is more contentious than the fate of Taiwan, which functions as an independent nation in all but official recognition by most of the world.

The People’s Republic of China has claimed Taiwan since the defeated Nationalist forces of Chiang Kai-shek retreated there in 1949, but in recent months Beijing has grown increasingly vocal in criticizing U.S. efforts to strengthen the island’s democracy and its military defenses.

Beijing’s assertive language is often coupled with displays of its growing military prowess. It has menaced Taiwan with military exercises simulating an amphibious assault and air patrols that have swept through the island’s air defense identification zone. Many military analysts, including some in the Pentagon, believe that the maneuvers by an increasingly well-equipped Chinese military could be a prelude to an invasion.

The Biden administration, like the Trump administration before it, has warned China that its military operations and threats are dangerous. The United States, which withdrew its official recognition of Taiwan as a condition of re-establishing relations with China in 1979, has responded by stepping up diplomatic efforts to bolster President Tsai Ing-wen of Taiwan.

That has included visits by officials and lawmakers, as well as weapon sales.

China says those efforts stoke popular sentiment in Taiwan to formally declare independence, which Beijing has warned would lead to war. Wariness in China intensified when President Biden answered a question at a televised town hall last month by declaring, imprecisely, that the United States was committed to Taiwan’s defense in the case of an attack.

It was unclear whether President Biden and Mr. Xi directly discussed the question of how the United States would respond, militarily, should Beijing attack Taiwan. The White House’s readout about the virtual meeting only described President Biden as affirming the United States’ position on Taiwan. The statement used longstanding language that acknowledges but does not recognize Beijing’s claim on Taiwan while indicating Beijing should do nothing to change the status quo.

Beijing is likely to be skeptical of the Biden administration’s intentions. “China’s view is that the United States plays rhetorical games on the Taiwan issue, saying that there is one China and that it does not support Taiwan independence, while it makes actual deals with Taiwan,” said Wu Xinbo, director of the center for American studies at Fudan University in Shanghai. “I think this is still a major divergence point in bilateral relations.”

Reporting and research by Steven Lee Myers and Li You.

From China’s perspective, the virtual meeting itself amounts to a vindication of its strategy to wait out the new administration.

After the tumult of the Trump years, China’s leaders hoped to reset the relationship with the United States when President Biden took office in January. When that didn’t happen, officials seemed surprised, then angry.

Senior officials lashed out as Mr. Biden’s national security team challenged China on a variety of issues — from Taiwan to the western Chinese region of Xinjiang, where the State Department has declared a genocide of Uyghurs and other predominantly Muslim ethnic minorities is underway. In a speech in Beijing in July celebrating 100 years of the Chinese Communist Party, China’s leader, Xi Jinping, warned: “The Chinese people will never allow foreign forces to bully, oppress or enslave us. Whoever nurses delusions of doing that will crack their heads and spill blood on the Great Wall of steel built from the flesh and blood of 1.4 billion Chinese people.”

What Beijing did not do was compromise on any of its policy and behaviors that have stoked exactly those divisions, including menacing military patrols and exercises around Taiwan. Instead, it squeezed concessions out of the United States.

Those included the release in September of Meng Wanzhou, an executive of the telecommunications giant Huawei who had been detained in Canada in 2018 on an American arrest warrant. Beijing, infuriated by the detention at the time, retaliated by essentially taking two Canadians hostage.

China continues to warn the United States of its red lines, especially over the fate of Taiwan, but the tone of various public statements has mellowed considerably. That is also in China’s interest heading into the Winter Olympics in Beijing in February and the 20th National Congress of the Communist Party in November.

“I think that both countries want to bring down the temperature,” said Ali Wyne, an analyst focused on U.S.-China relations with the Eurasia Group, a consultancy based in Washington. “They both recognize that threshold between intensifying competition and unconstrained rivalry is tenuous.”

President Biden and Xi Jinping, China’s top leader, made no apparent progress on trade issues at their virtual summit, but they struck a hopeful note about the potential for future deals.

Some of the differences were on display in the accounts the two sides released after the meeting. Mr. Biden repeated U.S. calls for China to live up to its agreement early last year to import more American goods, a senior administration official said. An official Chinese statement did not mention the agreement publicly, but it said Mr. Xi described the bilateral trade relationship as “mutually beneficial” while calling for trade not to be politicized.

There was no announcement of multi-billion-dollar commercial purchases of American products of the sort that Donald J. Trump, the former president, had sought from China. Trade officials from both sides would hold more talks, the senior administration official said.

The softer tone of the rhetoric on both sides in recent weeks and at the virtual summit has nonetheless inspired some optimism, particularly in China, on economic issues.

“I think gradually trade disputes will be resolved,” said Chen Dingding, a professor of international relations at Jinan University in Guangzhou. “We’ll see some concrete measures very soon.”

Wide differences between the two countries remain, including about the commitments the two sides made in striking their trade war truce early last year. That truce, dubbed the Phase 1 trade agreement, called for China to buy $380 billion worth of American goods by the end of 2021. But based on China’s purchases through September of this year, the country is on track to buy only three-fifths of that, according to data compiled by the Peterson Institute for International Economics in Washington.

China has bought large quantities of American corn, pork and other farm goods, but far fewer manufactured goods and far less fossil fuels than were called for by the Phase 1 agreement. That is partly because China has not placed large orders lately for Boeing jets, as air travel slowed during the pandemic. China has also been cautious about signing long-term agreements to buy American natural gas.

China is reportedly close to allowing Boeing 737 Max jets to return to its skies after crashes about three years ago in Ethiopia and Indonesia. The Federal Aviation Administration approved the plane late last year, and it has since been widely used elsewhere without incident.

China’s statement did not mention jetliners, but did say that Mr. Xi had called for closer cooperation on natural gas, although there were no details.

There have also been some hints of compromise on the American side. Katherine Tai, the U.S. trade representative, announced last month that the Biden administration would restart a Trump-era procedure for excluding a few specific products from tariffs. The exemptions are for products that American companies can prove that they genuinely need and cannot readily purchase elsewhere.

China was allowed to retain some tariffs on U.S. goods under the Phase 1 agreement, but has already issued exemptions for most of its tariffs.

Mr. Biden’s economic deputies are traveling elsewhere in Asia this week, strengthening ties to counterbalance the Chinese relationship. Ms. Tai and Commerce Secretary Gina M. Raimondo are touring the region, meeting with economic officials in Japan, Singapore, Malaysia, South Korea and India.

When President Biden connected with the Chinese leader, Xi Jinping, on a video call late Monday, each did so from two of the best-known rooms in their respective country’s statecraft.

Despite the physical distance from which the two talked, the choice of setting underscored the importance of the meeting and the attention to diplomatic protocol, even in an era of Zoom calls and coronavirus.

President Biden called from the Roosevelt Room, a famed meeting area in the White House, which President Nixon in 1969 renamed for Presidents Theodore Roosevelt and Franklin Roosevelt. Today, the room is frequently used to announce nominations and as a preparatory room for delegations before meeting the president.

Mr. Xi dialed in from the East Hall in China’s Great Hall of the People, a room featuring a large mural of a mountain landscape with a poem from Mao Zedong, the founder of the People’s Republic of China. That room is perhaps best known as the place where new members of the country’s Politburo Standing Committee are announced. The Great Hall of the People is a cavernous structure of ornate rooms built alongside Tiananmen Square in Beijing; it is where the Chinese Communist Party and China’s government stage their most important meetings.

In a video broadcast before the meeting, Kang Hui, an anchor for China’s state television broadcaster, pointed out that the East Hall has been the site of many high-profile state visits, and more recently has been the staging ground for Mr. Xi to virtually connect in meetings with other leaders and major conferences.

With strict protocols and lengthy quarantines in place to prevent the spread of Covid-19 across China’s borders, Mr. Xi has not left the country in almost two years.

During the summit, President Biden was candid about his concerns about the state of human rights in China, administration officials said.

Xi Jinping, China’s most authoritarian leader in decades, has been accused of overseeing a widespread rollback of individual freedoms across the country. According to the official readout from the Chinese government, he defended Beijing’s political model and said that while China was willing to discuss human rights, it would not be lectured by outsiders. “We do not approve of interfering in other countries’ internal affairs through human rights issues,” he told Mr. Biden.

China has drawn scrutiny from Western democracies over its crackdown in Xinjiang, where the authorities have rounded up and detained Uyghurs and other Muslim minorities in large numbers, and in Hong Kong, where a harsh national security law has undone many of the city’s democratic traditions.

The Biden administration has stuck by the Trump administration’s accusations of genocide in Xinjiang, and more recently, also raised concerns over the fate of Zhang Zhan, a citizen journalist whose family and friends say is critically ill in prison. Ms. Zhang is being held for documenting the chaos of the early days of the outbreak of the coronavirus in Wuhan.

President Biden has worked quickly to enlist allies to join his campaign to pressure China on issues such as human rights and trade. The U.S. Secretary of State, Antony Blinken, said this year that Beijing was routinely undercutting Hong Kong’s autonomy, and that the Biden administration would push back against what he described as coercion from China.

Mr. Xi has previously dismissed what Beijing sees as sanctimonious preaching.

When the United States imposed sanctions on Chinese officials over Hong Kong and Xinjiang, Beijing retaliated with its own penalties. Beijing has also responded to the recriminations with its own criticisms. Chinese diplomats and state media hit out at the United States over the chaotic withdrawal from Afghanistan.

It remains to be seen how firmly Mr. Biden will push Mr. Xi on human rights. In the first face-to-face meeting of American and Chinese officials of Biden’s administration in Alaska, the raising of such issues led to mutual denunciations, setting the tone for a testy relationship.

Climate policy is the rare area where the United States and China at least appear to be on the same page. At the United Nations climate summit in Glasgow this month, the two countries — the biggest polluting nations — signed a surprise pact to do more to cut emissions this decade.

During the summit on Monday, they reiterated their commitment to the issue, with the United States in its readout saying that the “two leaders discussed the existential nature of the climate crisis to the world.”

But much remains unclear about how the two governments will work together. The Glasgow pact was short on specifics, including any commitment from China on when it will start reducing the amount of carbon dioxide and other gases it generates by burning coal, gas and oil. Beijing has said only that it will do so by 2030.

China’s top leader Xi Jinping said climate policy could become a “new highlight” of cooperation with the United States, according to China’s statement on the summit. But Mr. Xi also reiterated Beijing’s position that China, as the world’s largest developing nation, had different responsibilities to uphold when it came to climate change than the developed countries that pumped out more carbon dioxide over the past century.

China’s mighty manufacturing sector makes it the planet’s No. 1 emitter, responsible for around a quarter of all global emissions. It is also the reason Beijing’s leaders cannot dial back emissions easily or quickly.

Electricity demand is still growing rapidly in China. And the world still depends on Chinese factories to produce electronics, toys, exercise equipment and much else.

Mr. Xi has announced steps to reduce China’s use of coal, the dirtiest fossil fuel. But the country still has extensive plans for building coal-fired power plants and for mining more coal, a need that has been highlighted by recent power shortages caused partly by a lack of coal. China already digs up and burns more of the fuel than the rest of the world.

Although China has been racing to put up wind and solar projects, it has not been able to shift from coal toward natural gas, which emits less carbon dioxide when burned, as quickly as the United States.

Lurking beneath the many tensions between Beijing and Washington is the question of whether the two countries are slipping into a Cold War, or something quite different.

One of the few areas of agreement between Xi Jinping, China’s leader, and President Biden is that letting relations devolve into Cold War behavior would be a mistake of historic proportions.During the talks, Mr. Xi implicitly criticized Mr. Biden’s efforts to shore up alliances of democratically minded countries to counter China, saying that “ideological demarcations” would “inevitably bring disaster to the world,” according to an official readout of his comments at the meeting. “The consequences of the Cold War are not far away,” the statement said.

Mr. Biden has insisted that the United States is not seeking a new Cold War. His national security adviser, Jake Sullivan, said last week, “we have the choice not to do that.” The summit meeting between the two leaders is part of a White House effort to make sure that the right choices are made — and that accidents and misunderstandings do not propel either country in the wrong direction.

There are many reasons to argue that what is happening today is quite different from the Cold War. The amount of economic interchange, and entanglement, between the United States and China is huge; with the Soviet Union it was minuscule. Both sides would have a huge amount to lose from a Cold War; Mr. Xi and Mr. Biden both know that and have talked about the risks.

Other deep links — the mutual dependencies on technology, information and raw data that leaps the Pacific in milliseconds on American and Chinese-dominated networks — also never existed in the Cold War.

“The size and complexity of the trade relationship is underappreciated,” Mr. Biden’s top Asia adviser, Kurt M. Campbell, said in July as part of his argument of why this moment significantly differs from the Cold War of 40 years ago.

Still, with his repeated references this year to a generational struggle between “autocracy and democracy,” Mr. Biden has conjured the ideological edge of the 1950s and ’60s. And so has Mr. Xi at moments, with his talk about assuring that China is not dependent on the West for critical technologies, while also trying to make sure that the West is dependent on China.

Without question, the past several months have resounded with echoes of Cold War behavior: the Chinese air force running sorties in Taiwan’s air identification zone; Beijing expanding its space program, launching three more astronauts to its space station and accelerating its tests of hypersonic missiles meant to defeat U.S. defenses; and the release of a top Huawei executive for two Canadians and two Americans in what looked like a prisoner swap.

At the same time, the United States announced that it would provide nuclear submarine technology to Australia, with the prospect that its subs could pop up, undetected, along the Chinese coast. It did not escape Chinese commentators that the last time the United States shared that kind of technology was in 1958, when Britain adopted naval reactors as part of the effort to counter Russia’s expanding nuclear arsenal.

That the summit was taking place virtually, not in person, was a concession to China’s leader, Xi Jinping.

The White House had hoped that he and President Biden would meet at the Group of 20 gathering in Rome last month, but Mr. Xi did not attend. He has not left China since Mr. Biden took office in January — in fact, not since January 2020, when the coronavirus was beginning to spread from China.

The ostensible reason for remaining home still seems to be Covid-19, but some experts have speculated that Mr. Xi could not afford to be away before an important political gathering that ended last week.

He used that forum to solidify his stature within the Communist Party, bolstering his case for what is widely expected to be a third five-year term as China’s paramount leader, beginning next year. With the coronavirus still a threat, it is conceivable that Mr. Xi might stay home until the party’s national congress next November.

That reflects more than just internal political machinations. It is in keeping with China’s increasing insularity, forged by a growing confidence — hubris, some might say — that the country under Mr. Xi’s leadership is the master of its own destiny, less dependent on the rest of the world for validation as its economic and military might solidifies.

Still, Mr. Xi’s absence has coincided with the withering of China’s international standing, with public sentiment in many countries turning against the country’s behavior at home and abroad. He faced sharp criticism for submitting a letter to the climate talks in Glasgow and for joining India in watering down the final statement to reduce pressure on cutting the use of coal.

Ever since President Nixon stunned the United States in 1971 by announcing that he would travel to China, meetings between American and Chinese leaders have become milestones in a relationship fraught with hope.

In the five decades that have followed, the relationship between the two countries has lurched between cooperation and confrontation. In 1979, Mao Zedong’s successor, Deng Xiaoping, met President Carter in Washington to normalize diplomatic ties and end years of mutual hostility.

That was followed by meetings with Ronald Reagan in 1982 and George H.W. Bush in February 1989 — that one just months before Deng ordered a brutal military crackdown on student protests around Tiananmen Square in Beijing.

Mr. Bush responded to the massacre by suspending all official contacts with the Chinese, but a month later surreptitiously dispatched his national security adviser, Brent Scowcroft, to keep open channels with a country then allied with the United States’ efforts to contain its Cold War rival, the Soviet Union.

There was not another official visit until 1997, when President Clinton played host to Jiang Zemin, who emerged as the country’s leader after Deng’s death, which officials hoped would usher in a new era of openness.

After a while, meeting with Chinese leaders and senior officials became a goal in itself of American foreign policy. The idea was that regular meetings would entwine the Chinese economy with the world’s.

In 2006, President George W. Bush and Hu Jintao announced the creation of a strategic economic dialogue, where officials from both sides could meet regularly to resolve proliferating trade disputes.

When President Obama came to office, the strategic economic dialogue in 2009 became the strategic economic and security dialogue, reflecting emerging conflicts over China’s expansionism in the South China Sea.

A criticism of both the George W. Bush and Obama administrations was that the Chinese smothered the Americans with talk, while doing as they pleased — whether cyberattacks, or militarization of artificial islands in the South China Sea.

U.S.-China summitry may have peaked in 2017. President Trump invited Xi Jinping to his Mar-a-Lago resort in April, where he informed him over “the most beautiful chocolate cake you’ve ever seen” that the United States had bombed Syria.

The two leaders met again that November, when Mr. Trump traveled to Beijing, becoming the first foreign leader to dine in the Forbidden City. “You’re a very special man,” he told Mr. Xi, banking on flattery to win over the Chinese leader. It didn’t.

The long-smoldering clash between China and the United States over the future of technology hit a rare moment of accord in September, when the Justice Department helped broker a deal that led to the release of a senior executive at the Chinese telecom equipment maker, Huawei.

The two countries have been struggling to find any more common ground in that area.

President Biden has done little to roll back measures put in place under the Trump administration aimed at limiting China’s access to American technology. U.S. officials fear China will use American software and equipment to build government-supported rivals and develop tools to strengthen its surveillance state, including advanced computers, artificial intelligence and facial recognition systems.

Huawei itself remains a point of contention. American authorities helped secure the release of Meng Wanzhou, the Chinese executive who was detained in Canada. But they are still restricting Huawei’s access to critical American semiconductors and software, crimping its business.

While parts of the Biden Administration have called for improving economic ties, many American lawmakers are pushing for even tougher measures on Chinese technology firms. Mr. Biden has invoked competition with China to help pass his infrastructure bill, which seeks to bolster American technology competitiveness.

On China’s side, the country’s drive for self-reliance will likely take precedence over taking steps to regain access to American technology. Beijing is unlikely to back away from its tough limits on the flow of data or free expression online. Those positions have effectively locked most major foreign internet firms out of China. One of the last, LinkedIn, said last month it would shut down there.