That evidence includes newly revealed radio transmissions intercepted by German intelligence in which Russian forces discussed carrying out indiscriminate killings north of Kyiv, the capital, according to two officials briefed on an intelligence report. Russia has denied any responsibility for atrocities.

Together, the steps announced Thursday represented a significant increase in efforts led by Western nations to isolate and inflict greater economic pain on Russia as its troops regroup for a wave of attacks in eastern Ukraine, prompting urgent calls by Ukrainian officials for civilians there to flee.

“These next few days may be your last chance to leave!” the regional governor of Luhansk, Serhiy Haidai, declared in a video on Facebook. “The enemy is trying to cut off all possible ways to leave. Do not delay — evacuate.”

But the Western penalties were unlikely to persuade Russia to stop the war, and they revealed how the allies were trying to minimize their own economic pain and prevent themselves from becoming entangled in a direct armed conflict with Moscow.

In some ways, the efforts underscored internal tensions among Russia’s critics over how best to manage the next stage of the conflict, which has created the biggest refugee crisis in Europe since World War II. The war is also indirectly worsening humanitarian and economic problems far from Ukraine, including rising food and energy prices that are exacerbating hunger and inflation, particularly in developing nations.

It took two days of protracted talks in Brussels for the European Union to approve a fifth round of sanctions against Russia that included its first ban on a Russian energy source, coal. But the measures were softened by several caveats, highlighting Europe’s diminishing appetite to absorb further economic fallout from the war.

The ban would be phased in over four months, instead of three as originally proposed, according to E.U. diplomats. Germany had been pushing for a longer transition period to wind down existing contracts, even though Russian coal is easier to replace with purchases from other suppliers, compared with oil and gas.

European diplomats also agreed to ban Russian-flagged vessels from E.U. ports, block trucks from Russia and its ally, Belarus, from E.U. roads, and stop the import of Russian seafood, cement, wood and liquor and the export to Russia of quantum computers and advanced semiconductors.

Ukrainian officials had urged Western nations to go further and completely cut off purchases of Russian oil and gas, contending that existing sanctions would not cripple Russia’s economy quickly or severely enough to affect President Vladimir V. Putin’s campaign to subjugate Ukraine by force.

“As long as the West continues buying Russian gas and oil, it is supporting Ukraine with one hand while supporting the Russian war machine with the other hand,” Ukraine’s foreign minister, Dmytro Kuleba, said Thursday at NATO headquarters in Brussels, where he urged members of the alliance to accelerate promised help to Ukraine’s outgunned military.

The NATO secretary general, Jens Stoltenberg, said the alliance would “further strengthen and sustain our support to Ukraine, so that Ukraine prevails in the face of Russia’s invasion.” But he did not offer details.

At the United Nations, the General Assembly’s resolution suspending Russia from the Human Rights Council, a step advocated by the United States and its allies, was the strongest measure the organization has taken to castigate the Kremlin.

Although the decision carries little practical impact, Russia’s suspension, approved on a 93 to 24 vote, with 58 countries abstaining, was still a diplomatic slap that Russia, one of the United Nations’ founding members, had hoped to avoid.

“The country that’s perpetrating gross and systematic violations of human rights should not sit on a body whose job it is to protect those rights,” Antony J. Blinken, the secretary of state, said at NATO headquarters.

Russia, which resigned its seat on the Human Rights Council in protest, denounced the vote as “an attempt by the U.S. to maintain its domination and total control” and to “use human rights colonialism in international relations.”

China, Cuba, North Korea, Iran, Syria and Vietnam were among the countries that joined Russia in opposing the measure, while India, Brazil, South Africa and Mexico were among those that abstained. Some of those countries argued the move could worsen the war, and called for further investigation of reports of Russian atrocities.

The last country to lose its seat on the panel was Libya in 2011, after President Moammar al-Qaddafi launched a ferocious crackdown on antigovernment protesters.

Russia remains one of five permanent members of the United Nations Security Council with a veto power that it has already used to block a resolution calling on it to stop the war and withdraw its forces.

As U.N. members were deliberating, the United States Senate voted unanimously to strip Moscow of its preferential trade status and to ban the import of Russian energy into the United States. The legislation would allow the United States to impose higher tariffs on Russian goods. Russian energy, however, represents only a small fraction of American imports, and Moscow is already having trouble exporting its oil.

The House approved the bills later on Thursday, sending them to President Biden, who was expected to sign them.

The latest efforts to punish Russia over the Feb. 24 invasion were energized partly by international outrage over the discovery of many dead civilians by Ukrainian soldiers who reclaimed areas north of Kyiv that had been vacated by retreating Russian forces.

Ukraine’s president, Volodymyr Zelensky, has said hundreds of bodies including children were found, many of them in the suburb of Bucha, and that many victims had been bound, tortured and shot in the head.

Mr. Kuleba, Ukraine’s foreign minister, was asked at NATO headquarters about reports of atrocities that may have been committed by Ukrainian troops.

He said he had heard about, but not seen, a video showing a group of Ukrainian soldiers killing captured Russian troops outside a village west of Kyiv. The video has been verified by The New York Times.

Mr. Kuleba said his country’s military observes the rules of warfare and would investigate any “isolated incidents” of atrocities.

“You don’t understand how it feels that Russian soldiers rape children,” he said. “This is not an excuse to those who violate the rules of warfare on either side of the front line. But there are some things which you simply can’t understand. I’m sorry.”

Mr. Blinken spoke with disgust about the atrocities attributed to Russian soldiers, saying “the sickening images and accounts coming out of Bucha and other parts of Ukraine have only strengthened our collective resolve.”

“The revulsion against what the Russian government is doing is palpable,” he said.

Russia has described evidence of the Bucha killings by Russian forces — including satellite images verified by The New York Times that show bodies on streets while still under Russian occupation — as fabricated.

Mr. Kuleba said the expected Russian assaults on the eastern regions of Luhansk and Donetsk made it more urgent that NATO members expedite delivery of weapons to help Ukraine defend itself.

“The discussion is not about the list of weapons,” Mr. Kuleba said. “The discussion is about the timeline. When do we get them?”

Mr. Blinken did not offer any new details on military assistance.

He noted that the United States had supplied Ukraine with arms for months, totaling more than $1.7 billion since Russia’s invasion began. That aid includes an additional $100 million worth of Javelin anti-tank missiles that the Biden administration approved for shipment this week.

Mr. Blinken expressed skepticism about the peace talks between Russia and Ukraine, saying he had “heard nothing from the Russians suggesting that they’re serious” about a negotiated settlement.

The mayor of the eastern city of Sloviansk, Vadim Lyakh, said it was “preparing for the worst” and stocking bomb shelters and hospitals with medical supplies and food.

“We have been watching closely how the Russians have encircled and seized nearby cities like Mariupol and Izium,” he said referring to two Ukrainian cities devastated by Russian attacks. “It’s clear that these cities were not evacuated in time, but in Sloviansk we have some notice, and that’s why we are actively pushing people to leave.”

Matina Stevis-Gridneff and Steven Erlanger reported from Brussels and Michael Levenson from New York. Reporting was contributed by Jane Arraf from Lviv, Ukraine, Thomas Gibbons-Neff from Kharkiv, Ukraine, Cora Engelbrecht and Megan Specia from Krakow, Poland, Ivan Nechepurenko from Istanbul, Catie Edmondson from Washington, Michael Crowley from Brussels, Farnaz Fassihi from New York and Nick Cumming-Bruce from Geneva.