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 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 Monday.

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 steady infusion of Western arms, both eastern Ukraine and Mariupol in the south have borne the brunt of a remorseless ground and artillery attack.

"Russian occupation forces are conducting intense fire along the entire line of contact and trying to hit artillery deep into the defences of Ukrainian troops," Ukrainian defence ministry spokesman Oleksandr Motuzyanyk told reporters.

The fighting is fiercest 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," President Volodymyr 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 also 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.

A total of 1,908 Ukrainian troops have surrendered this week at the steelworks, according to Russia's defence ministry, after releasing a video showing bedraggled defenders being taken into captivity.

Ukraine's Azov battalion commander Denys Prokopenko said only the dead remained.

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

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

Ukraine wants 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.

The International Committee of the Red Cross urged both sides to grant it access to prisoners of war and civilian internees, "wherever they are held".

"Many more families need answers," it said in a statement.

In Washington, Pentagon spokesman John Kirby said all prisoners of war should "be treated in accordance with the Geneva Convention and the law of war".

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

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.

- Underground living -

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

Biden offered "full, total, complete backing" to Finland and Sweden in their bid to join the NATO military alliance, when he welcomed their leaders to the White House on Thursday.

But all 30 existing NATO members need to agree on any new entrants, and Turkey has condemned the historically non-aligned Nordic neighbours' alleged toleration of Kurdish militants.

Shoigu said the Kremlin would respond to any NATO expansion by creating more military bases in western Russia.

Russia's own expansion in Ukraine has ebbed around the northeastern city of Kharkiv, its troops forced to retreat from a rearguard offensive by defending forces.

But Kharkiv remains in Russia artillery range, and hundreds of people are refusing to leave the relative safety of its metro system.

"We're tired. You can see what home comforts that we have," said Kateryna Talpa, 35, pointing to mattresses and sheets on the ground, and some food in a cardboard box.

She and her husband Yuriy are doing their best to cope in the Soviet-era station called "Heroes of Labour", alongside their cats Marek and Sima.

"They got used to it," Talpa said.

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