Between 7,000 and 8,000 civilians are still in Sievierodonetsk, in hiding, because it is too dangerous to leave, its mayor, Oleksandr Stryuk said on television.
"The military shares medicines with them," he said. "The destruction has increased. As the line of battle passed through the old part of the city, then this part is now in ruins. The Russians are destroying the foundations of the buildings."
The regional governor said, however, that the troops could hold out.
"This is a small town - 4 km by 4 km (2.5 miles by 2.5 miles) - a cosy and very homely square- yet into the fourth month they cannot capture it," Luhansk Governor Serhiy Gaidai said on television.
Ukraine has begged Western countries for more heavy weaponry, including advanced rocket systems, to hold off Russia's offensive, now concentrated in the east after Russian forces failed to seize Kyiv following the Feb. 24 invasion.
The United States, European Union nations and Britain have all promised such weapons, but Ukraine says deliveries have been too slow.