STORY: An officer from Pokrovsk who was distributing aid 31 miles (50 km) away in Krasnohorivka said there were many children in need of aid and the police were doing all they could to provide food and drinks.
In nearby Marinka, local residents have been sheltering in basements, unable to leave on their own.
Police offered to evacuate a group of residents on Thursday, first to Pokrovsk and on to Dnipro.
Many residents don't want to leave what's left of their properties, a police officer said, but they would help anyone who wanted to leave.
After being pushed back from the outskirts of Kyiv in May, Russia's troops have focused their efforts on capturing the entirety of the Donbas, an eastern industrial region where fighting has focussed in recent weeks on Sievierodonetsk, now largely in ruins.