Moscow claimed control of the strategic port city of Mariupol last month after a weeks-long siege, but hundreds of Ukrainian soldiers remained holed up in underground tunnels beneath the huge Azovstal industrial zone.
"Over the past 24 hours, 265 militants laid down their arms and surrendered, including 51 heavily wounded," the Russian defence ministry said.
Publishing images showing wounded soldiers being carried on stretchers, it said the injured were taken to a hospital in a part of the eastern Donetsk region controlled by pro-Kremlin rebels.
Elsewhere, lawmakers in Finland -- which shares a 1,300-kilometre (800-mile) border with Russia -- voted overwhelmingly in favour of joining the NATO military alliance.
The vote paves the way for a joint application with Sweden to be submitted on Wednesday, amid fears they could be the next targets of Russian aggression.
Meanwhile Kyiv said negotiations with Russia on ending the near three-month war, which has killed thousands and sent millions fleeing, were "on hold", blaming Moscow for failing to compromise.
Ukraine's defence ministry confirmed the soldiers had left Azovstal, expressing hope for an "exchange procedure... to repatriate these Ukrainian heroes as quickly as possible".
For those remaining in the warren of tunnels underneath the steelworks complex, it said it was doing "everything necessary for their rescue" -- although a military intervention was not possible.
In Moscow, Kremlin spokesman Dmitry Peskov did not answer questions about whether the Azovstal soldiers would be treated as war criminals or prisoners of war.
President Vladimir Putin "guaranteed that they would be treated according to the relevant international laws," he said.
Ukraine has accused Moscow of war crimes during the conflict, notably in the town of Bucha near Kyiv, where AFP reporters saw at least 20 bodies lying in the streets after Russian forces withdrew in late March.
The International Criminal Court said Tuesday it was deploying its largest-ever field team to Ukraine, comprising 42 investigators, forensic experts and support staff.
Trying to stay alive
The army said holding the steelworks had delayed the transfer of 20,000 Russian troops to other parts of Ukraine and stopped Moscow from quickly capturing the southern city of Zaporizhzhia.
"Azovstal defenders ruined Russia's plan to capture the east of Ukraine... This completely changed the course of the war," tweeted presidential aide Mykhaylo Podolyak.
"83 days of Mariupol defence will go down in history as the Thermopylae of the 21st century," he said, referring to the famous last stand by the Spartans against the Persians in 480 BCE.
Across the country, Ukrainian forces have managed to fight the huge Russian army for longer than many expected, fortified by weapons and cash from Western allies.
After circling the capital Kyiv in the early weeks of the war, Moscow has focused increasingly on the eastern region of Donbas, bordering Russia.
Ukrainian officials say Russian troops are withdrawing from around Kharkiv, the country's second-largest city, to be redeployed to Donbas.
But Kyiv's gains have come at a high cost, with villages gutted and destroyed by bombs.
In Ruska Lozova, just north of Kharkiv, Rostislav Stepanenko recounted to AFP how he had gone back to collect some belongings but returned empty-handed and stunned by the incessant artillery fire.
Asked what he did for a living, he joked that he was "trying to stay alive".
And his age? "Hopefully, I will be 54, but today I wouldn't expect that," he said with a nervous smile.
'Shelling without stopping'
Ukraine says Russia is targeting cities in Donbas including Severodonetsk, the easternmost city held by Ukrainian forces.
Control of Severodonetsk would grant the Kremlin de facto control of Lugansk, one of two regions -- along with Donetsk -- that comprise Donbas.
Russia's attempt to completely encircle Severodonetsk has been repelled, with Ukrainian forces blowing up railway bridges to slow their advance.
But Lugansk regional governor Sergiy Gaiday has said it was being shelled "without stopping" and two buildings at the city's general hospital had been hit overnight.
"We have 10 dead and three wounded in the region," he wrote on Telegram.
Elsewhere, eight people were killed and 12 injured in Russian strikes on the village of Desna, in northeastern Chernigiv region, where a Ukrainian military base is located, emergency services said.
Meanwhile in the town of New York, north of Donetsk, residents say they have been under artillery fire for a month, and it is getting worse.
"Now they are shooting at us from the west, east and south," seamstress Valentyna Kanebalotskaya told AFP.
NATO bids 'no direct threat'
Fearful of Russia's ambitions, Sweden and Finland are poised to give up decades of military non-alignment and join NATO.
Putin said on Monday the move posed "no direct threat for us... but the expansion of military infrastructure to these territories will certainly provoke our response".
His reaction was more moderate than comments earlier by deputy foreign minister Sergei Ryabkov, who called the expansion a "grave mistake with far-reaching consequences".
The NATO bids must be unanimously approved by the alliance's 30 nations, and Turkish President Recep Tayyip Erdogan on Monday voiced his objection.
He accused Finland and Sweden of harbouring terror groups, including outlawed Kurdish militants.
But US Secretary of State Antony Blinken voiced confidence that the bids would succeed and is due to meet Turkey's foreign minister in Washington on Wednesday.
As well as practical support for Ukraine, Western nations have sought to punish Russia with unprecedented economic sanctions, with the EU currently mulling a ban on Russian oil.
Hungary is blocking the ban, citing the cost, and Putin on Tuesday claimed Europe risked committing "economic suicide".
Many EU nations are also dependent on Russian gas but are in a quandary after Moscow demanded payment in rubles to circumvent the sanctions.
Italian energy giant Eni announced a potential workaround Tuesday involving opening two accounts with Russian energy firm Gazprom's bank. It proposed making payments in euros which would be converted into rubles through the Moscow stock exchange.