Hundreds of Ukrainian soldiers who held off Russian fighters at the besieged Azovstal steelworks in Mariupol have surrendered, Moscow said Tuesday, as Kyiv called for an immediate prisoner swap.

The strategic port city fell to Russian forces last month, but a relentless Ukrainian military unit held out in the maze of tunnels under the plant, hailed as heroes and celebrated for stalling Moscow's invasion.

The ministry, which published images showing soldiers on stretchers, said the injured were transported to a hospital in the eastern Donetsk region controlled by pro-Kremlin rebels.

The defence ministry in Kyiv said it was hoping for an "exchange procedure... to repatriate these Ukrainian heroes as quickly as possible".

The government would do "everything necessary" to rescue the undisclosed number of personnel still holed up in the Soviet-era bunkers, the ministry said, but admitted there was no military option available.

The fate of the captured Ukrainians was unclear Tuesday, with Kremlin spokesman Dmitry Peskov refusing to say whether they would be treated as criminals or prisoners of war.

President Vladimir Putin "guaranteed that they would be treated according to the relevant international laws," Peskov said.

Russian forces stand accused of committing war crimes during a conflict that has left thousands dead and forced millions to flee their homes.

These include the summary killing of civilians in places like Bucha, a small town outside of Kyiv, where AFP reporters witnessed bodies abandoned in the streets by retreating Russian invaders.

The International Criminal Court said Tuesday it was deploying its largest-ever field team to Ukraine, with 42 investigators, forensic experts and support staff being sent into the field to gather evidence of alleged crimes.

And the US State Department also announced it was creating a special unit to research, document and publicise Russian war crimes.

The Conflict Observatory will "capture, analyse, and make widely available evidence of Russia-perpetrated war crimes and other atrocities in Ukraine," the department said.

- NATO membership –

Moscow's invasion has galvanised a broad coalition of western nations, with Europe and the United States supplying weapons and support to Ukraine, but it has also sparked fears among countries on Russia's periphery about where Putin will set his sights next.

Finland and Sweden will on Wednesday formally submit a joint application to become members of NATO, the US-led western military alliance established to hold back Soviet Russia.

The application comes after lawmakers in Finland -- which shares a 1,300-kilometre (800-mile) border with Russia -- voted overwhelmingly in favour of joining the bloc.

Although both countries have long cooperated with NATO, they have spent decades formally unaligned.

Russia's invasion of Ukraine has galvanised public support for membership, which would guarantee an overwhelming military response from NATO members if Finland is attacked.

The two bids must be unanimously approved by the alliance's 30 nations, but Turkish President Recep Tayyip Erdogan has objected, accusing the Nordic nations of harbouring terror groups sympathetic to Kurdish separatists.

US Secretary of State Antony Blinken has voiced confidence the bids will succeed and is due to meet Turkey's foreign minister in Washington Wednesday.

- 'Trying to stay alive' -

The defence of Azovstal has symbolized Ukraine's plucky resistance against a much larger invading force, with Kyiv's troops holding out longer than many expected, fortified by weapons and cash from Western allies.

But the defence has not been without its price: whole villages have been razed, and their inhabitants left with nothing.

In Ruska Lozova, just north of Kharkiv, Rostislav Stepanenko told 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 he was "trying to stay alive".

In a phone call Tuesday, French President Emmanuel Macron told his Ukrainian counterpart Volodymyr Zelensky that arms deliveries from Paris would "increase in intensity" in the coming weeks.

Zelensky said the two leaders also discussed fuel supplies to Ukraine, ways to export Ukrainian agricultural products and Kyiv's application to join the European Union, which Macron has said could take decades.

- Strategic shift -

Russia's strategy has shifted considerably since its initial invasion, when troops tried to encircle Kyiv, in what was thought to be an attempt to decapitate the democratically elected government.

Ukrainian officials say Russian troops are now withdrawing from around Kharkiv, the country's second-largest city.

Forces are instead being deployed around the eastern region of Donbas, where Moscow-backed separatists have been fighting a guerilla war for years.

Targets include Severodonetsk, the easternmost city held by Ukrainian forces, the capture of which would give the Kremlin de facto control of Lugansk, one of two regions -- along with Donetsk -- that comprise Donbas.

Russia's attempt to surround Severodonetsk has been repelled, with Ukrainian forces blowing up railway bridges to slow the advance.

But the city was being shelled ceaselessly, with at least 10 people killed in fresh Russian strikes Monday, according to regional authorities.

Meanwhile, the West' campaign to isolate Russia economically continued to stutter, with a European Union plan to ban Russian oil imports stimied by EU-member Hungary.

Putin said Tuesday that Europe risked "economic suicide" if it turned off the taps.

Global oil prices have swung wildly in recent months, and inflation is rising in many parts of the world, partly because of the war in Ukraine.