Russian troops entered the outskirts of the Ukrainian city of Sievierodonetsk, a regional governor said on Monday, describing the fighting as "very fierce" in a city that become a key objective for Moscow's offensive in the Donbas.

Axar.az reports citing foreign media that shelling killed two civilians and wounded five others as Russian troops advanced into the city's southeastern and northeastern areas fringes, Luhansk region Governor Serhiy Gaidai said.

Incessant shelling has left Ukrainian forces defending ruins in Sievierodonetsk, but their refusal to withdraw has slowed a massive Russian offensive across the Donbas region in eastern Ukraine.

"Some 90% of buildings are damaged. More than two-thirds of the city's housing stock has been completely destroyed. There is no telecommunication," Ukrainian President Volodymyr Zelenskiy said in a televised speech.

"Capturing Sievierodonetsk is a fundamental task for the occupiers ... We do all we can to hold this advance."