Russia has suffered setbacks on the battlefield as Ukraine drives its troops out of the region around the second-largest city of Kharkiv, the fastest advance since forcing the Kremlin's forces from Kyiv and the northeast over a month ago.

Reuters journalists have confirmed Ukraine is now in control of territory stretching to the banks of the Siverskiy Donets River, around 40km east of Kharkiv.

Footage released by Ukrainian Airborne Forces Command appeared to show several burnt out military vehicles and segments of a bridge partially submerged in the river. The images showed many more damaged or abandoned vehicles, including tanks, in the woods and on the track leading to the river.

Delivering a daily intelligence update on Friday, Britain's defence ministry said the images suggested that Russia had lost armoured manoeuvre elements of at least one battalion tactical group and the pontoon bridging equipment depolyed while crossing the Siverskyi Donets river west of Severodonetsk.

Reuters could not immediately verify the report, or when or where the clash took place.

The British defence ministry said Russia was investing significant military effort further south from Kharkiv, near Izium and Severodonetsk, and was attempting a breakthrough towards Sloviansk and Kramatorsk.

In the capital Kyiv, wives and relatives of Ukrainian fighters holed up in the Azovstal steel plant in the southern port of Mariupol marched and chanted for their rescue.

Russian forces have been bombarding the steelworks, the last bastion of Ukrainian defenders in a city almost completely controlled by Russia after a siege of more than two months.

Deputy Prime Minister Iryna Vereshchuk told 1+1 television that negotiations were under way for an evacuation, starting with the most badly wounded.

In Kyiv, a court is due on Friday to begin hearing the first war crime case since the war began in February. A Russian soldier is due to go on trial accused of murdering a civilian in Chupakhivka, in northeastern Ukraine, on February 28.

Renewed fighting around Snake Island in recent days may become a battle for control of the western Black Sea coast, according to some defence officials, as Russian forces struggle to make headway in Ukraine's north and east.

Ukraine said it had damaged a Russian navy logistics ship near the island, a small but strategic outpost, and set it on fire.

"Thanks to the actions of our naval seamen, the support vessel Vsevolod Bobrov caught fire - it is one of the newest in the Russian fleet," said Serhiy Bratchuk, a spokesman for the Odesa regional military administration.

Satellite imagery provided by Maxar, a private US-based company, showed the aftermath of what it said were probable missile attacks on a Russian Serna-class landing craft near the island, close to Ukraine's sea border with Romania.

As fighting continued around the country, wider diplomatic moves dialled up pressure on Russian President Vladimir Putin.

Foreign ministers from the G7 group of rich nations aim to give what Germany called a "powerful sign of unity" as they meet on Friday to discuss the conflict and fears that it could spill over into Moldova.

Finland's plan to apply for NATO membership, announced on Thursday, and the expectation that Sweden will follow suit, would bring about the expansion of the Western military alliance that Putin aimed to prevent.

Abandoning the neutrality they maintained throughout the Cold War would be one of the biggest shifts in European security in decades.

Moscow called Finland's announcement hostile and threatened retaliation, including unspecified "military-technical" measures.

Putin cited NATO's potential expansion as one of the main reasons he sent forces into Ukraine.

Australian Associated Press