"In the 21st century, such attacks against the civilian population are unthinkable and abhorrent," said Jan Lipavsky, foreign minister of the Czech Republic which holds the European Union's rotating presidency.
"We must not overlook it. We stand for the punishment of all war criminals," he added in a message on Twitter.
"I call for the speedy establishment of a special international tribunal that will prosecute the crime of aggression."
The appeal follows the discovery by Ukrainian authorities of around 450 graves outside the formerly Russian-occupied city of Izyum with most of the exhumed bodies showing signs of torture.
"Among the bodies that were exhumed today, 99 percent showed signs of violent death," Oleg Synegubov, head of Kharkiv regional administration, said on social media.
"There are several bodies with their hands tied behind their backs, and one person is buried with a rope around his neck," he added.
"Russia leaves only death and suffering. Murderers. Torturers," said Ukraine's President Volodymyr Zelensky. Some of the remains exhumed included children and people who were likely tortured before dying, he added.
US Secretary of State Antony Blinken on Friday said that the graves likely provided more evidence that Russia is committing war crimes in its pro-Western neighbour, and French President Emmanuel Macron said what happened in Izyum were atrocities.
"I condemn in the strongest terms the atrocities committed in Izyum, Ukraine, under Russian occupation," Macron tweeted.
'Tortured'
The Ukrainian parliament's human rights commissioner, Dmytro Lubinets, said there were "probably more than 1,000 Ukrainian citizens tortured and killed in the liberated territories of the Kharkiv region".
Ukraine national police chief Igor Klymenko said they had found multiple torture rooms in the town of Balakliya and elsewhere in Kharkiv since the Russians were driven out.
The United Nations in Geneva has said it hopes to send a team to determine the circumstances of the deaths.
The announcement of this macabre discovery has raised a new wave of indignation in the West.
The discoveries came a little more than five months after the Russian army, driven out of the vicinity of the Ukrainian capital Kyiv, left behind hundreds of corpses of civilians, many of whom bore the traces of torture and summary executions.
"Deeply shocked'
The European Union is "deeply shocked" at the discovery by Ukrainian officials of mass graves in the recaptured city of Izyum, the bloc's foreign policy chief Josep Borrell said Friday.
"This inhuman behaviour by the Russian forces, in total disregard of international humanitarian law and the Geneva conventions, must stop immediately.
On Thursday, EU chief Ursula von der Leyen said she wanted Russian President Vladimir Putin to face the International Criminal Court over war crimes in Ukraine.
In Washington, US President Joe Biden warned his Russian counterpart Vladimir Putin against using chemical or tactical nuclear weapons in the wake of serious losses in his war in Ukraine.
"Don't. Don't. Don't," Biden said, in an excerpt from an interview with CBS' "60 Minutes" aired Friday evening.
Biden was responding to an interviewer's question about the possibility of Putin, whose army is incurring heavy losses in the Ukraine counteroffensive this month, resorting to chemical or tactical nuclear weapons.
"You would change the face of war unlike anything since World War II," Biden said.
"They will become more of a pariah in the world, more than they have ever been," the US leader added.
'Pushing them back'
On the ground, Ukrainian forces have recaptured thousands of square kilometres in recent weeks thanks to a counter-offensive in the north-east and now threaten enemy positions in the south, as the fighting and bombings continue.
The Russians "are angry because our army is pushing them back in its counter-offensive," said Svitlana Shpuk, a 42-year-old worker in Kryvyi Rih, a southern town, and Zelensky's hometown, which was flooded after a dam was destroyed by Russian missiles.
The governor of the Kharkiv region, Oleg Synegoubov, said that an 11-year-old girl was killed by missile fire in the region.
Pavlo Kyrylenko, the governor of Donestk in eastern Ukraine which has been partially controlled by Russian-backed separatists since 2014, said on social media that Ukrainian firefighters were battling a fire there and that the bombing had led to cuts in drinking water.
"The occupiers are deliberately targeting infrastructure in the area to try to inflict as much damage as possible, primarily on the civilian population," he charged.
The Russian army denies targeting civilian infrastructure or residential areas.
In its daily briefing in Moscow, the Kremlin said it had carried out "high-precision" strikes against Ukrainian positions in the Mykolayev and Kharkiv regions.
In the relative calm of Kyiv on Saturday, hundreds of Ukrainians took part in a farewell ceremony at the Kiev national opera house for former ballet dancer and later teacher Oleksandr Shapoval, who was killed at the age of 47 in the east of the country while fighting the Russians.
Shapoval was hit by mortar fire on September 12, near the town of Mayorsk in the Donetsk region.
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