The Russian-battered eastern Ukrainian city of Sievierodonetsk appears to be on the brink of becoming another Mariupol as services and aid have been cut and Moscow seeks to capture all of Ukraine’s industrial Donbas region.

Fierce street fighting is under way in the city as Ukrainian defenders are trying to push the Russians out, Mayor Oleksandr Striuk told the AP in a phone interview.

Russian troops have advanced a few blocks toward the city centre, he said.

“The number of victims is rising every hour, but we are unable to count the dead and the wounded amid the street fighting,” the mayor added.

He said 12,000-13,000 civilians left in the city that once held more than 100,000 are sheltering in basements and bunkers to escape the Russian bombardment.

Russian forces stormed Sievierodonetsk after trying unsuccessfully to encircle it, Ukrainian officials said, and Ukrainian President Volodymyr Zelensky has described the situation there as “indescribably difficult”.

An intense Russian artillery barrage has destroyed critical infrastructure and damaged 90% of the buildings.

Sievierodonetsk, located 189 miles south of the Russian border, has emerged in recent days as the epicentre of the Donbas fighting. Mariupol is the city on the Sea of Azov that spent nearly three months under Russian siege before the last Ukrainian fighters surrendered.

Sievierodonetsk and Lysychansk span the strategically important Siverskiy Donetsk River.

They are the last major areas under Ukrainian control in the province of Luhansk, which makes up the Donbas together with the adjacent Donetsk region.

Russian foreign minister Sergei Lavrov told French TF1 television on Sunday that Moscow’s “unconditional priority is the liberation of the Donetsk and Luhansk regions”, adding that Russia sees them as “independent states”.

He also suggested other regions of Ukraine should be able to establish close ties with Russia.

The Ukrainian army reported heavy fighting around Donetsk, the regional capital, as well as Lyman to the north, a small city that serves as a key rail hub in the Donetsk region.

“The enemy is reinforcing its units,” the Ukrainian armed forces’ General Staff said. “It is trying to gain a foothold in the area.”

Mr Zelensky will address European Union leaders on Monday who are gathering in a new show of solidarity with Ukraine amid divisions over whether to target Russian oil in a new series of sanctions.

He has repeatedly demanded that the EU target Russia’s lucrative energy sector and deprive Moscow of billions of dollars each day in supply payments.

On Sunday Mr Zelenskyy visited soldiers in Kharkiv, Ukraine’s second-largest city, where Ukrainian fighters pushed Russian forces back from nearby positions several weeks ago.

Russia has kept up its bombardment of the north-eastern city from afar, and explosions could be heard shortly after Mr Zelensky’s visit.

Shelling and air strikes have destroyed more than 2,000 apartment buildings in the city since Russia invaded Ukraine on February 24, according to the regional governor, Oleh Syniehubov.

In a video address later on Sunday, Mr Zelensky praised Kharkiv regional officials but said he had fired the regional head of the country’s top security agency, the SBU, for his poor performance. In the wider Kharkiv region, Russian troops still held about one third of the territory, Mr Zelensky said.

In Luhansk, constant Russian shelling has created what provincial governor Serhiy Haidai called a “severe situation”.

But he said some Luhansk supply and evacuation routes functioned on Sunday. He claimed the Russians had retreated “with losses” around a village near Sievierodonetsk but conducted air strikes on another nearby river village.

Sievierodonetsk mayor Oleksandr Striuk has estimated that 1,500 civilians in the city have died since the war began, from Russian attacks as well as from a lack of medicine or treatment.

The Institute for the Study of War, a think tank based in Washington, questioned the Kremlin’s strategy of assembling a huge military effort to take Sievierodonetsk, saying it was proving costly for Russia and would bring few returns.