Serhiy Hayday said in a statement that 60 houses were destroyed in the region, and two people were found dead in the rubble.
He said one of the victims was a girl who died when a Russian shell hit a high-rise building in Lysychansk on Saturday, in a strike that injured four others. A cinema and 22 houses were also damaged in an air strike.
Separately, in an operational update on Sunday, the General Staff of the Armed Forces of Ukraine said Russia "carried out assault operations in the area of the city of Severodonetsk" where "the fighting continues."
In Sloviansk, about 60 kilometers (37 miles) to the west, Russia carried out "intensive reconnaissance" on the city, and on the outskirts, conducted air strikes on Dovhenke area, and also artillery shelling of civilian infrastructure in nearby Bohorodychne and Sviatohirsk, the Ukrainian army statement said.
Elsewhere, the military reported new Russian attacks on civilian infrastructure in towns and villages between Ukraine's second-largest city, Kharkiv, and the Russian border. Ruski Tyshky, Petrivka and Ternova, were among the locations hit. The Russian army has also been conducting remote mining in those areas, according to the statement.