Ukraine on Friday ordered its remaining troops holed up in Mariupol's besieged Azovstal steelworks to lay down their arms after nearly three months of desperate resistance.

Russia's flattening of the strategic port city has drawn multiple accusations of war crimes, including a deadly attack on a maternity ward, and Ukraine has begun a reckoning for captured Russian troops.

The first post-invasion trial of a Russian soldier for war crimes neared its closely watched climax in Kyiv, after 21-year-old sergeant Vadim Shishimarin admitted to killing an unarmed civilian early in the offensive. The verdict is due on May 23. 

Shishimarin told the court on Friday that he was "truly sorry" but his lawyer said in closing arguments that the young soldier was "not guilty" of premeditated murder and war crimes.

While Ukrainian forces fended off the Russian offensive around Kyiv, helped by a large infusion of Western arms, both eastern Ukraine and Mariupol in the south have borne the brunt of a ferocious ground and artillery attack.

President Volodymyr Zelensky's government received a fresh boost as the US Congress approved a $40-billion (38-billion-euro) aid package, including funds to enhance Ukraine's armoured vehicle fleet and air defence system.

And meeting in Germany, G7 industrialised nations pledged $19.8 billion to shore up Ukraine's shattered public finances.

Ukraine sorely needs enhanced capability to fend off the kind of onslaught Russia is waging in the eastern region of Donbas, a Russian-speaking area that has been partially controlled by pro-Kremlin separatists since 2014.

"In Donbas, the occupiers are trying to increase pressure," Zelensky said in his nightly video address late on Thursday. "There's hell -- and that's not an exaggeration."

In the eastern city of Severodonetsk, 12 people were killed and another 40 wounded by Russian shelling, the regional governor said.

Burial with honours 

Zelensky described the bombardment of Severodonetsk as "brutal and absolutely pointless", as residents cowering in basements described an unending ordeal of terror.

The city forms part of the last pocket of Ukrainian resistance in Lugansk, which along with the neighbouring region of Donetsk comprises the Donbas war zone.

Russian Defence Minister Sergei Shoigu said his forces' campaign in Lugansk was "nearing completion".

Also apparently complete is the capture of the Azovstal steelworks, a totemic symbol of Ukraine's dogged resistance since Russian President Vladimir Putin launched the invasion on February 24 to remove a Western-leaning, "Nazi" threat on his borders.

Russia released a video appearing to show exhausted Ukrainian soldiers trudging out of the sprawling steel plant, after weeks during which the besieged defenders and civilians huddled in tunnels, enduring shortages of food, water and medicine.

"The higher military command has given the order to save the lives of the soldiers of our garrison and to stop defending the city," Azov battalion commander Denys Prokopenko said in a video on Telegram.

He said efforts continued to remove killed fighters from the plant.

"I now hope that soon, the families and all of Ukraine will be able to bury their fighters with honours," he said.

Ukraine is hoping to exchange the surrendering Azovstal soldiers for Russian prisoners. But in Donetsk, the pro-Kremlin authorities are in turn threatening to put some of them on trial.

"Our expectation is ... that all prisoners of war will be treated in accordance with the Geneva Convention and the law of war," Pentagon spokesman John Kirby said in Washington.

US President Joe Biden has cast the Ukraine war as part of a great US-led struggle of democracy against authoritarianism.

Biden offered "full, total, complete backing" to Finland and Sweden in their bid to join the NATO military alliance, when he gave their leaders a red-carpet welcome at the White House on Thursday.