The Russian military said on Saturday its forces had captured another Ukrainian village in its slow advance westward through the Donetsk region.
And reports from the Kharkiv region in the northeast suggested Russian troops were closing in on the city of Kupiansk.
Russian forces struck Sloviansk and Kramatorsk - two cities Moscow will target as its forces press on with their westward drive.
Both towns have come under frequent attack since the Russian invasion of its neighbour in February 2022.
Donetsk region Governor Vadym Filashkin said one person died and three were injured in Sloviansk, with pictures posted online showing buildings reduced to rubble.
He said four multi-storey dwellings and 32 private homes were damaged.
In Kramatorsk, pictures posted by the city council showed heavy damage to part of an apartment building.
Officials said at least one person was trapped under rubble and several residents were injured.
A mass drone attack on the town of Nizhyn near the Russian border killed one person and damaged local infrastructure.
The Russian Defence Ministry said its forces had seized the village of Zaporizhzhia, southwest of Pokrovsk, where Ukrainian forces have been holding back Russian attacks for months.
Zaporizhzhia village is distinct from the Ukrainian city of Zaporizhzhia, the regional centre and large industrial hub located some 160km to the southeast.
The General Staff of Ukraine's armed forces on Friday listed the village as one of several where Kyiv's forces had repelled Russian attacks.
On Friday, the Russian Defence Ministry said it had captured the village of Moskovka, just outside the city of Kupiansk, also the target of repeated Russian attacks in recent months.
Both Russian and Ukrainian military bloggers have reported an upswing in fighting around Kupiansk in the past week.
The town was first occupied by Russian forces in the first weeks of the 2022 invasion, but recaptured by Ukrainian troops later in the year in a lightning counter-offensive.
