American officials, determined to keep secret their means of collecting the intelligence on Russia’s requests, declined to describe further the kind of military weapons or aid that Moscow is seeking. The officials also declined to discuss any reaction by China to the requests.

President Xi Jinping of China has strengthened a partnership with Mr. Putin and has stood by him as Russia has stepped up its military campaign, destroying cities in Ukraine and killing hundreds or thousands of civilians. American officials are watching China closely to see whether it will act on any requests of aid from Russia. Jake Sullivan, the White House national security adviser, is scheduled to meet on Monday in Rome with Yang Jiechi, a member of the Chinese Communist Party’s elite Politburo and director of the party’s Central Foreign Affairs Commission.

Mr. Sullivan intends to warn Mr. Yang about any future Chinese efforts to bolster Russia in its war or undercut Ukraine, the United States and their partners.

“We are communicating directly, privately to Beijing that there will absolutely be consequences for large-scale sanctions evasion efforts or support to Russia to backfill them,” Mr. Sullivan said on CNN on Sunday.

“We will not allow that to go forward and allow there to be a lifeline to Russia from these economic sanctions from any country anywhere in the world,” he said.

Mr. Sullivan did not make any explicit mention of potential military support from China, but other U.S. officials spoke about the request from Russia on the condition of anonymity because of the sensitivity of diplomatic and intelligence matters.

Liu Pengyu, a spokesman for the Chinese Embassy in Washington, said he had never heard of the request from Russia. “The current situation in Ukraine is indeed disconcerting,” he said, adding that Beijing wants to see a peaceful settlement. “The high priority now is to prevent the tense situation from escalating or even getting out of control.”

The Biden administration is seeking to lay out for China the consequences of its alignment with Russia and penalties it will incur if it continues or increases its support. Some U.S. officials argue it might be possible to dissuade Beijing from ramping up its assistance to Moscow. Chinese leaders may be content to offer rhetorical support for Moscow and may not want to further enmesh themselves with Mr. Putin by providing military support for the war, those U.S. officials say.

Mr. Sullivan said China “was aware before the invasion took place that Vladimir Putin was planning something,” but added that the Chinese might not have known the full extent of the Russian leader’s plans. “It’s very possible that Putin lied to them, the same way he lied to Europeans and others,” he said.

Mr. Xi has met with Mr. Putin 38 times as national leaders, more than with any other head of state, and the two share a drive to weaken American power.

Traditionally, China has bought military equipment from Russia rather than the other way around. Russia has increased its sales of weaponry to China in recent years. But China has advanced missile and drone capabilities that Russia could use in its Ukraine campaign.

Although Russia on Sunday launched a missile barrage on a military training ground in western Ukraine that killed at least 35 people, there has been some evidence that Russian missile supplies have been running low, according to independent analysts.

Last week, the White House criticized China for helping spread Kremlin disinformation about the United States and Ukraine. In recent days, Chinese diplomats, state media organizations and government agencies have used a range of platforms and official social media accounts to amplify a conspiracy theory that says the Pentagon has been financing biological and chemical weapons labs in Ukraine. Right-wing political figures in the United States have also promoted the theory.

On Friday, Russia called a United Nations Security Council meeting to present its claims about the labs, and the Chinese ambassador to the U.N., Zhang Jun, supported his Russian counterpart.

“Now that Russia has made these false claims, and China has seemingly endorsed this propaganda, we should all be on the lookout for Russia to possibly use chemical or biological weapons in Ukraine, or to create a false flag operation using them,” Jen Psaki, the White House press secretary, wrote on Twitter last Wednesday.

China is also involved in the Iran nuclear negotiations, which have stalled because of new demands from Russia on relief from the sanctions imposed by Western nations in response to the Ukraine war.

American officials are trying to determine to what degree China would support Russia’s position in those talks. Before Russia raised the requests, officials from the nations involved had been close to clinching a return to a version of the Obama-era nuclear limits agreement from which Donald J. Trump withdrew, Mr. Sullivan might bring up Iran with Mr. Yang on Monday.

Current and former U.S. officials say the Rome meeting is important given the lives at stake in the Ukraine war and the possibility of Russia and China presenting a geopolitical united front against the United States and its allies in the years ahead.

“This meeting is critical and possibly a defining moment in the relationship,” said Evan Medeiros, a Georgetown University professor who was a senior Asia director on the National Security Council during the Obama administration.

“I think what the U.S. is probably going to do is lay out the costs and consequences of China’s complicity and possible enabling of Russia’s invasion,” he said. “I don’t think anyone in the administration has illusions that the U.S. can pull China away from Russia.”

Some U.S. officials are looking for ways to compel Mr. Xi to distance himself from Mr. Putin on the war. Others see Mr. Xi as a lost cause and prefer to treat China and Russia as committed partners, hoping that might galvanize policies and coordination among Asian and European allies to contain them both.

Chinese officials have consistently voiced sympathy for Russia during the Ukraine war by reiterating Mr. Putin’s criticism of NATO and blaming the United States for starting the conflict. They have refrained from any mention of a Russian “war” or “invasion,” even as they express general concern for the humanitarian crisis.

They mention support for “sovereignty and territorial integrity,” a common catchphrase in Chinese diplomacy, but do not say explicitly which nation’s sovereignty they support — meaning the phrase could be interpreted as backing for Ukraine or an endorsement of Mr. Putin’s claims to restoring the territory of imperial Russia.

China and Russia issued a 5,000-word statement on Feb. 4 saying their partnership had “no limits” when Mr. Putin met with Mr. Xi before the opening ceremony of the Winter Olympics in Beijing. Around that time, senior Chinese officials asked senior Russian officials not to invade Ukraine before the end of the Games, according to U.S. and European officials who cite a Western intelligence report.

Starting last November, American officials quietly held talks with Chinese officials, including the ambassador in Washington and the foreign minister, to discuss intelligence showing Mr. Putin’s troop buildup to persuade the Chinese to tell the Russians not to launch a war, U.S. officials said. The Chinese officials rebuffed the Americans at every meeting and expressed skepticism that Mr. Putin intended to invade Ukraine, the U.S. officials said.

William J. Burns, the C.I.A. director, said Thursday in a Senate hearing that he believed Mr. Xi was “unsettled” by the Ukraine war.

Last Tuesday, Mr. Xi repeated China’s standard talking points on the war in a video call with the leaders of France and Germany. He also said that all nations should show “maximum restraint” and that China was “deeply grieved by the outbreak of war again on the European continent,” according to a Chinese readout. He did not say Russia had started the fighting.

U.S. and European officials say large Chinese companies will most likely refrain from openly violating sanctions on Russia for fear of jeopardizing their global commerce. On Thursday, some Russian news articles and commentary questioned China’s commitment to Russia after news agencies reported that China was refusing to send aircraft parts to the country.

Russia, as U.S. officials often remind the public, has relatively few friends or allies. And officials have said Russia’s outreach to its partners is a sign of the difficulties it is encountering trying to subdue Ukraine.

As the United States and Europe have increased pressure and sanctions, Moscow has sought more aid.

In the buildup to war, Russia got assistance from Belarus, using its territory to launch part of the invasion. Minsk has also tried to help Moscow evade sanctions. Those actions prompted the European Union to impose sanctions on Belarus. The penalties would limit money flowing into Belarus from Europe and block some Belarusian banks from using the SWIFT financial messaging system.

Michael Carpenter, the U.S. ambassador to the Organization for Security and Cooperation in Europe, accused Belarus of being a “co-aggressor” and having “stabbed your neighbor in the back,” referring to Ukraine.

President Aleksandr G. Lukashenko of Belarus has said his military will not join in the war. But Russia has launched missiles from Belarus and evacuated some injured Russian soldiers to hospitals in that country.

President Bashar al-Assad of Syria, who owes his government’s survival to Russian intervention in the Syrian civil war, also declared support for Moscow’s invasion. Russia has tried to recruit Syrian fighters to join the Ukraine war, according to the Pentagon.

While there are no details of how many recruits Moscow has enlisted or if they have arrived in Ukraine, American officials said it was an indicator of the strategic and tactical problems that have plagued Russian commanders.

Before the start of the war, European officials said, Russian military contractors with experience fighting in Syria and Libya secretly entered eastern Ukraine to help lay the groundwork for the invasion.