Ukrainian officials try to build pressure to hold Russia accountable for war crimes.

After its recent success in reclaiming territory in its northeast with a lightning offensive, Ukraine on Sunday tried to build support for holding Russia accountable for alleged war crimes.

Ukraine’s prosecutor general, Andriy Kostin, and its ambassador to the United States, Oksana Markarova, both spoke on Sunday on American television shows about what its troops were finding as they moved into towns after pushing the Russians out.

Mr. Kostin said that his office was investigating thousands of cases of possible war crimes, and that the recently uncovered evidence of mass graves in the city of Izium, which had been occupied by the Russians for months, pointed to a pattern.

“What we see now is, of course, the horrible amount of potential war crimes committed by Russian aggressor,” Mr. Kostin said in an interview on “Face the Nation” on CBS. He added, “And it seems that, for me, that whenever Russian Army comes, they turn this place into the new Bucha, as we see in Izium.”

He was referring to the torture, rape and execution of civilians by Russian soldiers that The New York Times documented in Bucha, a Kyiv suburb, and other cities around Ukraine in the spring, though the situation in the northeast is not identical.

The investigators working in Ukraine to build cases for war crimes face immense challenges. Complicating their efforts is the fact that they are working while the war is still raging. The Kremlin has denied allegations against its forces, and its spokesman, Dmitri S. Peskov, said on Monday that reports of Russian atrocities in Izium are “a lie,” Russia’s Interfax news agency reported.

Ms. Markarova, the Ukrainian envoy to the United States, in an appearance on ABC’s “This Week” on Sunday, said that Ukrainian fighters had come across evidence of “tortures, rapes, killings, war crimes of massive proportions.”

And President Biden referred to the actions by President Vladimir V. Putin of Russia over seven months of war as “barbaric.”

“It has been barbaric what he has done,” he said in an interview with CBS that aired Sunday on “60 Minutes.”

Mr. Biden also warned the Russian president not to use chemical or tactical nuclear weapons in Ukraine, where Russian forces have been left reeling from their retreats on the battlefield. Some Western officials have expressed concern that a threatened Mr. Putin could lash out with an unconventional weapon.

“Don’t. Don’t. Don’t. You will change the face of war unlike anything since World War II,” Mr. Biden said, an apparent reference to the American use of nuclear weapons on Hiroshima and Nagasaki in Japan.

“They’ll become more of a pariah in the world than they ever have been,” Mr. Biden said of the Russians. He warned that the response would be “consequential” and would depend “on the extent of what they do.”

U.S. security officials appear more concerned than ever that Mr. Putin could escalate the war to compensate for his humiliating retreat from the northeastern Kharkiv region, after Ukraine gained more ground in a few days than Russia had in months.

On Sunday, the top U.S. military official voiced his concerns.

“The war is not going too well for Russia right now. So it’s incumbent upon all of us to maintain high states of readiness, alert,” Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, told reporters in Warsaw after visiting a base hosting U.S. troops, according to Reuters. “In the conduct of war, you just don’t know with a high degree of certainty what will happen next.”

President Volodymyr Zelensky will have a chance to make Ukraine’s case to world leaders this week when he addresses the United Nations General Assembly. The General Assembly voted on Friday to let him submit a pre-recorded speech to the gathering in New York, making an exception to its requirement that all leaders speak in person. His address is expected to be broadcast midweek.

Dan Bilefsky contributed reporting.