Pro-Moscow separatists claimed the last bridge out of Sievierodonetsk had been destroyed and Ukrainian defenders there must now surrender or die.

Ukraine said there was still another way out although it was severely damaged.

Ukraine has issued increasingly urgent calls for more Western weapons to help defend Sievierodonetsk, which Kyiv says could hold the key to the outcome of the battle for control of the eastern Donbas region and the future course of the war.

Regional governor Sergei Gadai said fighting was raging and Ukrainian forces were defending building by building.

"The battles are so fierce that fighting for not just a street but for a single high-rise building can last for days," he said on social media.

Russian forces now controlled about 70 per cent of Sievierodonetsk, he said, and were destroying it "quarter by quarter" in one of the bloodiest assaults since they launched their invasion on February 24.

"Russians continue to storm the city, having a significant advantage in artillery they have somewhat pushed back the Ukrainian soldiers," Gaidai, who is governor of the Luhansk region that includes Sievierodonetsk, said on Monday.

Russian artillery fire pummelled the Azot chemical plant, where hundred of civilians were sheltering, he said.

"About 500 civilians remain on the grounds of the Azot plant in Sievierodonetsk, 40 of them are children. Sometimes the military manages to evacuate someone," he said, noting the lack of a ceasefire agreement or agreement on evacuation corridors.

Gaidai said the twin city of Lysychansk across the Siverskyi Donets river to the west was also being shelled by Russian forces, and a six-year-old child had been killed there.

Russia's RIA news agency quoted a pro-Moscow separatist spokesperson, Eduard Basurin, as saying the last bridge over the river linking the two cities had been destroyed on Sunday. Ukrainian troops were effectively blockaded in Sievierodonetsk and should surrender or die, Basurin said.

Gaidai also said one crossing was destroyed on Sunday, but there was still another "half destroyed" bridge remaining, though it could not be used for heavy vehicles.

"If after new shelling the bridge collapses, the city will truly be cut off. There will be no way of leaving Sievierodonetsk in a vehicle."

As Mariupol fell to Russia last month, hundreds of civilians and badly wounded Ukrainian soldiers were evacuated after being trapped for weeks in the Azovstal steelworks there.

Ukrainian President Volodymyr Zelenskiy said in his nightly video address on Sunday that severe fighting was ongoing in the Donbas, "literally for every metre".

Attacks that resulted in child casualties had created a lasting image of Russia for the rest of the world.

"Not Peter the Great, not Lev Tolstoy, but children injured and killed in Russian attacks," he said, an apparent reference to Russian President Vladimir Putin's remarks last week comparing Moscow's military campaign to Russian emperor Peter the Great's 18th century conquest of lands held by Sweden.

In Sievierodonetsk, the last pocket of Ukrainian land held in the Luhansk region, Ukrainian and Russian forces were both suffering heavy losses, Roman Vlasenko, head of Sievierodonetsk district administration, told local TV.

"Our boys are holding on but the conditions are tough," he said. Vlasenko said the city had been without communications and normal services for a month.

Ukrainian Presidential Adviser Mykhailo Podolyak issued the latest appeal for more weaponry, boiling it down into a list of equipment he said was needed for heavy weapons parity, including 1,000 howitzers, 500 tanks and 1,000 drones.

"We are waiting for a decision," he said, adding that Western defence ministers would meet on Wednesday in Brussels.

Russia issued the latest of several recent reports saying it had destroyed US and European arms and equipment, hoping to send the message that delivering more would be futile.

Russia's defence ministry said high-precision air-based missiles had struck near the railway station in Udachne northwest of Donetsk, hitting equipment that had been delivered to Ukrainian forces.

Australian Associated Press