The Kremlin has warned of retaliatory "military-technical" steps after Finland's leaders came out in favour of applying to join Nato.

Sweden is expected to follow its Nordic neighbour within days as part of a historic realignment triggered by Russia's invasion of Ukraine.

Meanwhile, the first war crimes trial of a Russian soldier since the start of the conflict is set to open on Friday in Kyiv.

A 21-year-old captured member of a Russian tank unit is accused of fatally shooting a civilian during the opening week of the war.

On the ground, Russian forces pounded areas in central, northern and eastern Ukraine, including the last pocket of resistance in Mariupol, as part their offensive to take the industrial Donbas region. Ukraine has recaptured some towns and villages in the north-east.

Two and a half months after Russia's invasion of Ukraine sent a shiver of fear through Moscow's neighbours, Finland's president and prime minister announced that the Nordic country should apply right away for membership in Nato, the military defence pact founded in part to counter the former Soviet Union.

Finnish President Sauli Niinisto said this week: "You (Russia) caused this. Look in the mirror."

While the country's parliament still has to weigh in, the announcement means Finland is all but certain to apply and gain admission, though the process could take months to complete.

Sweden, likewise, is considering putting itself under Nato's protection.

That would represent a major change in Europe's security landscape. Sweden has avoided military alliances for more than 200 years, while Finland adopted neutrality after its defeat by the Soviets in the Second World War.

Public opinion in both nations shifted dramatically in favour of Nato membership after the invasion, which stirred fears in countries along Russia's flank that they could be next.

Such an expansion of the alliance would leave Russia surrounded by Nato countries in the Baltic Sea and the Arctic and would amount to a stinging setback for Russian President Vladimir Putin, who had hoped to divide and roll back Nato in Europe but is instead seeing the opposite happen.

Nato Secretary-General Jens Stoltenberg has said the alliance would welcome Finland and Sweden with open arms.

Russia's foreign ministry warned that Moscow "will be forced to take retaliatory steps of military-technical and other characteristics in order to counter the emerging threats to its national security".

Nato's funnelling of weapons and other military support to Ukraine already has been critical to Kyiv's surprising success in tackling the invasion, and the Kremlin warned anew in chilling terms that the aid could lead to direct conflict between Nato and Russia.

"There is always a risk of such conflict turning into a full-scale nuclear war, a scenario that will be catastrophic for all," said Dmitry Medvedev, deputy head of Russia's Security Council.

In other developments, Ukrainian officials said their forces took out another Russian ship in the Black Sea.

The Vsevolod Bobrov logistics ship was struck as it was trying to deliver an anti-aircraft system to Snake Island, said Oleksiy Arestovych, an adviser to the Ukrainian President.

He said the ship was badly damaged but was not believed to have sunk. A spokesman for the Odesa regional military administration said the vessel caught fire after the strike.

There was no confirmation from Russia and no reports of casualties.

In April, the Ukrainian military sank the Moskva cruiser, the flagship of the Black Sea fleet, and in March it destroyed the landing ship Saratov.

While Russia's advance in the Donbas has been slow, its forces have gained some ground and taken some villages.

Four civilians were killed on Thursday in three communities in the Donetsk region, which is part of the Donbas, the regional governor reported.

The UK Ministry of Defence said Russia's focus on the Donbas has left its remaining troops around the north-eastern city of Kharkiv vulnerable to counter-attack from Ukrainian forces, which recaptured several towns and villages around the city.

Russian strikes killed at least two civilians on the outskirts of Kharkiv, Ukraine's second-largest city, local authorities said.

The attacks also damaged a building housing a humanitarian aid unit, municipal offices and hospital facilities, Vyacheslav Zadorenko, the mayor of the suburban town of Derhachi, wrote in a Telegram post.

None of the sites "had anything to do with military infrastructure", the mayor said.

Ukraine also said Russian forces had fired artillery and grenade launchers at Ukrainian troops around Zaporizhzhia, which has been a refuge for civilians fleeing Mariupol, and attacked in the Chernihiv and Sumy regions to the north.

Overnight air strikes near Chernihiv, in northern Ukraine, killed at least three people, Ukraine's military said. It said that Russian troops fired rockets at a school and student dormitory in Novhorod-Siversky and that some other buildings, including private homes, were also damaged.

In his evening address to the nation, Ukrainian President Volodymyr Zelensky condemned the assaults.

"Of course, the Russian state is in such a state that any education only gets in its way," he said.

"But what can be achieved by destroying Ukrainian schools? All Russian commanders who give such orders are simply sick and incurable."