Russia says the flagship of its Black Sea fleet was seriously damaged and its crew evacuated following a fire that caused an explosion, while Ukraine insists the vessel was hit by missiles.

The incident on the Moskva missile cruiser occurred after ammunition on board blew up, the Interfax news agency quoted the Russian defence ministry as saying.

“As the result of a fire on the Moskva missile cruiser, ammunition detonated,” it said in a statement.

Russia said the 500-strong crew was all evacuated.

But Maksym Marchenko, the governor of the region around the Black Sea port of Odesa, said in an online post the 12,500-tonne ship was hit by two missiles, without providing evidence.

“Neptune missiles guarding the Black Sea caused very serious damage,” he said in an online post.

Reuters was not able to independently verify either account.

The ship – described as the most important in Russia’s Black Sea fleet – is the same one that attacked Ukraine’s Snake Island in February. A recording of the Moskva ordering the Ukrainian outpost on the island to surrender, and the succinct reply – “Russian warship, go f— yourself” – went viral at the time.

Ukraine warned late on Wednesday that Russia was ramping up efforts in the country’s south and east as it sought full control of Mariupol, in what would be the first major city to fall.

Western governments are sending more military aid to bolster Kyiv.

Russia’s defence ministry said on Wednesday 1026 soldiers from Ukraine’s 36th Marine Brigade, including 162 officers, had surrendered in Mariupol, which has been besieged for weeks, and that the port was fully under its control.

Capturing the city’s Azovstal industrial district, where the marines have been holed up, would give the Russians full control of Ukraine’s main Sea of Azov port, reinforce a southern land corridor and expand its occupation of the country’s east.

Ukraine’s general staff said Russian forces were attacking Azovstal and the port. But a defence ministry spokesman said he had no information about any surrender.

“Russian forces are increasing their activities on the southern and eastern fronts, attempting to avenge their defeats,” Ukraine’s President Volodymyr Zelensky said in a Wednesday night video address.

The US on Wednesday announced an extra $US800 million ($A1.1 billion) in military assistance, including artillery systems, armoured personnel carriers and helicopters. France and Germany also pledged more.

Russia will view US and NATO vehicles transporting weapons on Ukrainian territory as legitimate military targets, Deputy Foreign Minister Sergei Ryabkov told the TASS news agency.

Ukraine says tens of thousands of people are believed to have been killed in Mariupol and accuses Russia of blocking aid convoys to civilians marooned there.

Its mayor, Vadym Boichenko, said Russia had brought in mobile crematoria “to get rid of evidence of war crimes” – a statement that was not possible to verify.

Moscow has blamed Ukraine for civilian deaths and accused Kyiv of denigrating Russian armed forces.

In the village of Lubianka, north-west of Kyiv, from where Russian forces had tried and failed to subdue the capital before being driven away, a message to Ukrainians had been written on the wall of a house that had been occupied by Russian troops.

“We did not want this … forgive us,” it said.

The Kremlin says it launched a “special military operation” to demilitarise and “liberate” Ukraine, a message villagers said had been repeated to them by Russian troops.

“To liberate us from what? We’re peaceful … We’re Ukrainians,” Lubianka resident Viktor Shaposhnikov said.

Poland’s President Andrzej Duda said on a visit to Kyiv with his Lithuanian, Latvian and Estonian counterparts that those who had committed and ordered crimes must be brought to justice.

The Kremlin denounced US President Joe Biden’s description of Moscow’s actions in Ukraine as amounting to genocide, with spokesman Dmitry Peskov saying it was unacceptable from the leader of a country he said had committed crimes of its own.

An initial report from the Organisation for Security and Co-operation in Europe documents a “catalogue of inhumanity” by Russian troops in Ukraine, according to the US ambassador to the OSCE.

“This includes evidence of direct targeting of civilians, attacks on medical facilities, rape, executions, looting and forced deportation of civilians to Russia,” Michael Carpenter said.

Russia has denied targeting civilians and has said Ukrainian and Western allegations of war crimes are fabricated.

The Kyiv district police chief said 720 bodies had been found in the region from where Russian forces had retreated, with more than 200 people missing.

-with AAP