Ukraine on Friday ordered its last troops holed up in Mariupol's Azovstal steelworks to lay down their arms, while Russia said its months-long operation to capture the strategic port city is now complete.

Russia's flattening of Mariupol has drawn multiple accusations of war crimes, including over a deadly attack on a maternity ward, and Ukraine has begun a legal 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.

- 'End of the operation' -

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.

Moscow on Friday said the battle for the Azovstal steelworks -- a totemic symbol of Ukraine's dogged resistance since Russian President Vladimir Putin launched the invasion on February 24 -- was now over.

Russian defense ministry spokesman Igor Konashenko said 2,439 Ukrainian personnel had surrendered at the steelworks since May 16, the final 500 on Friday.

Shoigu had informed Putin of "the end of the operation and the complete liberation of the (Azovstal) industrial complex and the city of Mariupol", Konashenko added.

Ukraine's Azov regiment commander Denys Prokopenko had earlier 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".

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

The US Congress this week 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 invasion of 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 Russian 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.

Latest developments

Here are the latest developments in the war in Ukraine:

- Russia homes in on Lugansk -

Russian Defence Minister Sergei Shoigu says Moscow is nearing full control of the separatist region of Lugansk in eastern Ukraine.

"The liberation of the Lugansk People's Republic is nearing completion," Shoigu says.  

After some 2,000 Ukrainian soldiers surrendered at the besieged Azovstal steel plant in the port city of Mariupol, now under Moscow's control, Kyiv orders its remaining troops holed up there to lay down their arms after nearly three months of desperate resistance.

- 'Hell' in Donbas -

The renewed Russian offensive in Donbas has turned the eastern Ukrainian region into "hell", President Volodymyr Zelensky says.

"In Donbas, the occupiers are trying to increase pressure," he says.

In his nightly address, he adds: "There's hell, and that's not an exaggeration."

- New Russian bases -

Shoigu also says Moscow will create new military bases in western Russia in response to the expansion of NATO. 

"By the end of the year, 12 military units and divisions will be established in the Western Military District," Shoigu tells a meeting. 

- Soldier's lawyer urges acquittal -

The lawyer for the first Russian soldier on trial in Kyiv says his client is "not guilty" of premeditated murder and war crimes, urging his acquittal, even though he has admitted to killing a civilian.

Sergeant Vadim Shishimarin, at the centre of the first war crimes trial held over the conflict, has said he is "truly sorry" and asked the widow of the Ukrainian civilian he killed for forgiveness.

Ukrainian prosecutors have requested he be given a life sentence.

- German no to EU fund -

Germany's finance minister is ruling out any joint EU borrowing to help cover the massive cost of rebuilding war-scarred Ukraine, after the idea was floated by top European officials.

After chairing G7 talks in Germany that saw countries pledge nearly $20 billion (19 billion euros) in aid to Ukraine, Christian Lindner said there would be no repeat of the EU's landmark post-pandemic recovery fund, known as "Next Generation", that is being financed by common debt.

- Turkey 'determined' to block NATO bids -

President Recep Tayyip Erdogan says he is talking to Western leaders about Turkey's objections to NATO membership for Sweden and Finland, whom he accuses of sheltering Kurdish separatists. 

Russia's war in Ukraine has shifted political opinion in both Nordic countries in favour of joining the Western military alliance. 

"We cannot say 'yes' to (Sweden and Finland)... joining NATO, a security organisation," Erdogan said.

- Russia to cut gas to Finland -

Russian supply of natural gas to Finland is to be cut on Saturday morning, Finnish and Russian energy companies say, after the country refused to pay supplier Gazprom in rubles.

"We have been carefully preparing for this situation," Finland's Gasum CEO Mika Wiljanen says. "There will be no disruptions in the gas transmission network."

- Strike on cultural centre -

Zelensky says Russian strikes gutted a cultural centre in eastern Ukraine and wounded eight people, including a child.

In a statement on social media, Zelensky says that Russian strikes had targeted "the newly-renovated House of Culture", in the town of Lozova, in the eastern region of Kharkiv.