Ukrainian President Volodymyr Zelenskiy said Russia's siege of the port city of Mariupol was "a terror that will be remembered for centuries to come".
"Over the past week, several thousand Mariupol residents were deported onto the Russian territory," the city council said in a statement on its Telegram channel late on Saturday.
Reuters could not independently verify the claim.
Russian news agencies have said buses have carried several hundred people Moscow calls refugees from the strategic port on the Sea of Azov to Russia in recent days.
Air raid sirens sounded across major Ukrainian cities early on Sunday but there were no immediate reports of fresh attacks.
Some 400,000 people have been trapped in Mariupol for more than two weeks, sheltering from heavy bombardment that has severed central supplies of electricity, heating and water, according to local authorities.
Rescue workers were still searching for survivors in a Mariupol theatre that local authorities say was flattened by Russian air strikes on Wednesday. Russia denies hitting the theatre or targeting civilians.
On Friday, Russia's defence ministry said its forces were "tightening the noose" around Mariupol and that fighting had reached the city centre.
In a late night broadcast, Zelenskiy said the siege of Mariupol would "go down in history of responsibility for war crimes".
"To do this to a peaceful city... is a terror that will be remembered for centuries to come."
Still, he said, peace talks with Russia were needed although they were "not easy and pleasant".
The UN human rights office said at least 847 civilians had been killed and 1,399 wounded in Ukraine as of Friday. The Ukrainian prosecutor general's office said that 112 children have been killed.
Russian forces have taken heavy losses since February 24, when President Vladimir Putin launched what he calls a "special operation" aimed at demilitarizing Ukraine and purging it of what he sees as dangerous nationalists. Ukraine and the West say Putin launched an aggressive war of choice.
Long columns of troops that bore down on the capital Kyiv have been halted in the suburbs.
Ukraine's military said Russian forces did not conduct offensive operations on Saturday, focusing instead on replenishing supplies and repairing equipment. It also said Ukrainian air defences shot down three Russian combat helicopters.
Zelenskiy said the Ukrainian front line was "simply littered with the corpses of Russian soldiers".
Reuters could not independently verify the situation on the ground.
In Syria, some paramilitary fighters say they were ready to deploy to Ukraine to fight in support of their ally Russia but have not yet received instructions to go.
On Saturday, Russia said its hypersonic missiles had destroyed a large underground depot for missiles and aircraft ammunition in the western Ivano-Frankivsk region. Hypersonic weapons can travel faster than five times the speed of sound, and the Interfax agency said it was the first time Russia had used them in Ukraine.
A spokesperson for the Ukrainian Air Force Command confirmed the attack, but said the Ukrainian side had no information on the type of missiles used.
Russian Foreign Minister Sergei Lavrov said Moscow expected its operation in Ukraine to end with the signing of a comprehensive agreement on security issues, including Ukraine's neutral status, Interfax reported.
Kyiv and Moscow reported some progress in talks last week toward a political formula that would guarantee Ukraine's security, while keeping it outside NATO, though each sides accused the other of dragging things out.
Zelenskiy has said Ukraine could accept international security guarantees that stopped short of its longstanding aim to join NATO. That prospect has been one of Russia's primary stated concerns.
The Ukrainian president, who makes frequent impassioned appeals to foreign audiences for help, told an anti-war protest in Bern on Saturday that Swiss banks were where the "money of the people who unleashed this war" lay and their accounts should be frozen.
Ukrainian cities "are being destroyed on the orders of people who live in European, in beautiful Swiss towns, who enjoy property in your cities. It would really be good to strip them of this privilege," he said in an audio address.
Neutral Switzerland, which is not a member of the European Union, has fully adopted EU sanctions against Russian individuals and entities, including orders to freeze their wealth in Swiss banks.
The EU measures are part of a wider sanctions effort by Western nations aimed at squeezing Russia's economy and starving its war machine.
US President Joe Biden warned his Chinese counterpart, Xi Jinping, on Friday of "consequences" if Beijing gave material support to Russia's invasion of Ukraine.
On Saturday, Chinese Foreign Minister Wang Yi said China stood on the right side of history over the Ukraine crisis.
"China's position is objective and fair, and is in line with the wishes of most countries. Time will prove that China's claims are on the right side of history," Wang told reporters, according to a statement published by his ministry on Sunday.