US President Joe Biden will host the leaders of Finland and Sweden on Thursday to discuss their NATO membership bids, while Ukraine said no military option was left to rescue the soldiers still inside a steel plant besieged by Russian forces.

Moscow's troops have been accused of widespread atrocities against civilians during their devastating campaign, and Ukraine began its first war crimes trial of the conflict on Wednesday with a Russian soldier pleading guilty.

The brutality of the invasion that began on February 24 shook Sweden and Finland, and the neighbours -- after decades of military non-alignment -- decided to seek NATO membership despite warnings from the Kremlin.

This handout from the Russia's defence ministry shows Ukrainian soldiers being searched after leaving Azovstal This handout from the Russia's defence ministry shows Ukrainian soldiers being searched after leaving Azovstal Photo: Russian Defence Ministry via AFP / Handout

"I warmly welcome and strongly support the historic applications from Finland and Sweden for membership in NATO," Biden said in a statement Wednesday, offering US support against any "aggression" while their bids are considered.

Biden will meet President Sauli Niinisto of Finland and Sweden's Prime Minister Magdalena Andersson in Washington on Thursday for consultations.

Their bids face stiff resistance from NATO member Turkey, which accuses the two nations of harbouring anti-Turkish extremists.

But Western allies remain optimistic they can overcome Ankara's objections.

Fierce Ukrainian resistance has repelled the Russian invasion far more effectively than most initially expected Fierce Ukrainian resistance has repelled the Russian invasion far more effectively than most initially expected Photo: AFP / Yasuyoshi CHIBA

In an effort to lower the diplomatic heat, US Secretary of State Antony Blinken met with Turkey's Foreign Minister Mevlut Cavusoglu at the United Nations, who called the face-to-face discussion "extremely positive".

Applications for entry into the alliance require the approval of all members.

For now, several including Britain have offered security guarantees to Finland and Sweden to guard against any Russian aggression.

The International Criminal Court said Tuesday it was deploying its largest-ever field team to Ukraine The International Criminal Court said Tuesday it was deploying its largest-ever field team to Ukraine Photo: AFP / Yasuyoshi CHIBA

British Prime Minister Boris Johnson said these applications would not have been expected recently "but Putin's appalling ambitions have transformed the geopolitical contours of our continent".

On the ground, in the ruined port city of Mariupol, more than 1,000 Ukrainian soldiers including senior commanders remained inside the besieged Azovstal steel plant, a pro-Russian separatist leader said.

The reversal of Sweden's and Finland's longstanding policy of non-alignment came as the Russian war on Ukraine nears its third month The reversal of Sweden's and Finland's longstanding policy of non-alignment came as the Russian war on Ukraine nears its third month Photo: AFP / Jonathan NACKSTRAND

Moscow said 959 of the troops had surrendered this week.

Ukraine's defence ministry pledged to do "everything necessary" to rescue those still in the sprawling plant's tunnels but admitted there was no military option available.

Those who have left the heavily shelled plant were taken into Russian captivity, including 80 who were seriously wounded, Russia's defence ministry said.

Map showing number of people killed in fighting since the start of Russian invasion on February 24, recorded by the NGO Acled Map showing number of people killed in fighting since the start of Russian invasion on February 24, recorded by the NGO Acled Photo: AFP / Cléa PÉCULIER

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

But their fate was unclear, with Kremlin spokesman Dmitry Peskov refusing to say whether they would be treated as criminals or prisoners of war.

Mariupol has been devastated by Russian attacks, and a US official alleged Moscow's forces of committing atrocities in the city.

"Some Russian officials recognise that despite claiming to be 'liberators' of... Mariupol, Russian forces are carrying out grievous abuses... including beating and electrocuting city officials," the official said.

In Mariupol, more than 1,000 Ukrainian soldiers including senior commanders remain inside the besieged Azovstal steel plant as Russian soldiers patrol the outside of the sprawling complex In Mariupol, more than 1,000 Ukrainian soldiers including senior commanders remain inside the besieged Azovstal steel plant as Russian soldiers patrol the outside of the sprawling complex Photo: AFP / Olga MALTSEVA

Ukraine's President Volodymyr Zelensky hit out at Moscow in his nightly address to the nation, calling the invasion an "absolute failure".

"They are afraid to acknowledge that catastrophic mistakes were made at the highest military and state level," Zelensky said.

Despite their last-ditch resistance in places such as Mariupol and the successful defence of Kyiv, Ukrainian forces are retreating across swathes of the eastern front.

Vadim Shishimarin, a shaven-headed sergeant from Irkutsk in Siberia, is expected to be the first of many prosecuted by Ukraine Vadim Shishimarin, a shaven-headed sergeant from Irkutsk in Siberia, is expected to be the first of many prosecuted by Ukraine Photo: AFP / Genya SAVILOV

The losses often come after weeks of battles over towns and small cities that get pulverised by the time the Russians surround them in a slow-moving wave.

"I tell everyone that there is no reason to worry when the banging is from outgoing fire," Volodymyr Netymenko said as he packed up his sister's belongings before evacuating her from the burning village of Sydorove in eastern Ukraine.

"But when it is incoming, it is time to run. And things have been flying at us pretty hard for the past two or three days."

In the Russian region of Kursk, one person died and others were injured in an attack on a village on the border with Ukraine, the local governor said Thursday.

"Another enemy attack on Tyotkino, which took place at dawn unfortunately ended in tragedy," Roman Starovoyt said on Telegram.

Authorities in Russian border regions have repeatedly accused Ukrainian forces of launching attacks.

The conflict has sparked a massive exodus of more than six million Ukrainians, many bearing accounts of torture, sexual violence and indiscriminate destruction.

Ukraine's first trial for war crimes -- expected to be the first of many linked to the Russian invasion -- began in a cramped Kyiv courtroom on Wednesday.

Vadim Shishimarin, a shaven-headed Russian sergeant from Irkutsk in Siberia, pleaded guilty to a war crime and faces a life sentence.

Shishimarin admitted to shooting dead an unarmed 62-year-old man in Ukraine's Sumy region four days into the invasion.

"By this first trial, we are sending a clear signal that every perpetrator, every person who ordered or assisted in the commission of crimes in Ukraine shall not avoid responsibility," prosecutor general Iryna Venediktova said.

Russia's government has no information on the soldier, Kremlin spokesman Peskov said, adding that many such cases reported by Ukraine are "simply fake or staged".

The International Criminal Court is deploying its largest-ever field team to Ukraine, with 42 investigators, forensic experts and support staff to gather evidence of alleged war crimes.

In another step affirming US support for Ukraine, the American embassy in Kyiv reopened on Wednesday after three months.

The Kremlin meanwhile intensified a tit-for-tat round of diplomatic expulsions against European countries, ordering dozens of personnel from France, Italy and Spain to leave.

The Russian invasion has blown a hole in Ukraine's finances, as tax revenue has dropped sharply, leaving it with a shortfall of around $5 billion a month.

Finance ministers from G7 nations will meet in Germany on Thursday to try and find a solution for Kyiv's budget troubles.

Russia and Ukraine produce 30 percent of the global wheat supply.

UN Secretary-General Antonio Guterres said Wednesday that the conflict "threatens to tip tens of millions of people over the edge into food insecurity".

"Malnutrition, mass hunger and famine" could follow "in a crisis that could last for years," Guterres warned as he and others urged Russia to release Ukrainian grain exports.