If the Russians seize the Azovstal industrial district, where the marines have been holed up, they would be in full control of the port, the lynchpin between Russian-held areas to the west and east and providing a land corridor for Russian troops and supplies.
Reuters journalists accompanying Russian-backed separatists saw flames billowing from the Azovstal district on Tuesday.
Ukraine's general staff, in its morning report on Wednesday, said that Russian forces were proceeding with attacks on Azovstal and the port. Ukraine's defence ministry spokesman said he had no information about any surrender by marines.
Thousands are believed to have been killed under a near-seven week siege of the city and Russia has been massing thousands of troops in the area for a new assault, Ukrainian President Volodymyr Zelenskiy said.
Ukraine says tens of thousands of civilians have been trapped inside that city with no way to bring in food or water, and accuses Russia of blocking aid convoys.
Russia's defence ministry said that 1,026 soldiers of Ukraine's 36th Marine Brigade surrendered.
Chechen leader Ramzan Kadyrov, an ardent supporter of Russian President Vladimir Putin, also said more than 1,000 marines had surrendered and urged remaining forces holed up in the Azovstal steel mill to surrender.
"Within Azovstal at the moment there are about 200 wounded who cannot receive any medical assistance," Kadyrov said in a Telegram post. "For them and all the rest it would be better to end this pointless resistance and go home to their families."
Russian television showed pictures of what it said were marines giving themselves up at Illich Iron and Steel Works in Mariupol on Tuesday, many of them wounded.
It showed what it said were Ukrainian soldiers being marched down a road with their hands in the air. One of the soldiers was shown holding a Ukrainian passport.
BIDEN ACCUSES RUSSIA OF GENOCIDE
Russian forces have failed to capture one major city and have suffered heavy losses since invading Ukraine on Feb. 24.
Moscow's incursion, the biggest attack on a European state since 1945, has seen more than 4.6 million people flee abroad, killed or wounded thousands and left Russia increasingly isolated on the world stage.
The Kremlin says it launched a "special military operation" to demilitarise and "denazify" Ukraine. Kyiv and its Western allies reject that as a false pretext for an unprovoked attack.
The presidents of Poland, Lithuania, Latvia and Estonia were on their way to Kyiv to meet Zelenskiy, an adviser to the Polish leader said on Wednesday.
The four join a growing number of European politicians to visit the Ukrainian capital since Russian forces were driven away from the country's north earlier this month.
U.S. President Joe Biden said for the first time that Moscow's invasion of Ukraine amounted to genocide, as Putin said Russia would "rhythmically and calmly" continue its operation and achieve its goals.
Biden has repeatedly called Putin a war criminal, but the accusation of genocide was an escalation of his rhetoric.
"Yes, I called it genocide because it has become clearer and clearer that Putin is just trying to wipe out the idea of being able to be Ukrainian and the evidence is mounting," Biden told reporters as he prepared to board Air Force One on Tuesday.
Russia has denied targeting civilians and has said Ukrainian and Western allegations of war crimes are fabricated.
Many towns Russia has retreated from in northern Ukraine were littered with the bodies of civilians killed in what Kyiv says was a campaign of murder, torture and rape.
'CALM' OPERATION
Interfax Ukraine news agency on Wednesday quoted the Kyiv district police chief saying 720 bodies have been found in the region around the capital, with more than 200 people missing.
The General Headquarters of the Armed Forces of Ukraine said in a Wednesday briefing that Russian forces were maintaining rocket and bomb attacks on civilian infrastructure in the Kharkiv region in the northeast and the Zaporizhzhia region in central Ukraine. Reuters could not verify the reports.
Putin on Tuesday used his first public comments on the conflict in more than a week to say Russia would "rhythmically and calmly" continue its operation, and expressed confidence his goals, including on security, would be achieved.
Zelenskiy mocked Putin in an early morning address: "How could a plan that provides for the death of tens of thousands of their own soldiers in a little more than a month of war come about?"
Putin also said that on-off peace negotiations "have again returned to a dead-end situation for us".
Putin, who had been ubiquitous on Russian television in the early days of the war, had largely retreated from public view since Russia's withdrawal from northern Ukraine two weeks ago.
The assault on the industrial heartland of Donbas sets the stage for a protracted battle that is certain to inflict heavy losses on both sides and will ultimately define the course of the war, analysts said.
Ukrainian Deputy Defence Minister Hanna Malyar said there was a high risk of Russia using chemical weapons, echoing earlier warnings by Zelenskiy.
Chemical weapons production, use and stockpiling is banned under the 1997 Chemical Weapons Convention.
Russia denied using chemical weapons, saying it had destroyed its last chemical stockpiles in 2017.
(Reporting by Reuters bureaus; Writing by Michael Perry and Nick Macfie; Editing by Stephen Coates, Simon Cameron-Moore and Alex Richardson)
