Russian authorities said on Saturday that seven people were killed by Ukrainian shelling on the Russian border region of Belgorod.
Four bodies were pulled from the rubble of a partially collapsed apartment block in the town of Shebekino, the civil defence said.
One woman who was rescued later died in hospital, regional governor Vyacheslav Gladkov wrote on Telegram.
The building had been damaged on Friday after Ukrainian attacks on Shebekino some 5 kilometres from the border with Ukraine. Gladkov also reported one death each in the Russian towns of Oktyabrsky and Murom. Shebekino was shelled again on Saturday.
On the other side of the border sits the Ukrainian town of Vovchansk, around which Russian and Ukrainian troops are currently engaged in fierce fighting.
Russian units, supported by their air force continued their attacks in the area around Vovchansk on Saturday, the General Staff in Kiev said in its daily situation report in the evening.
Unusually strong Russian advances were also reported from the Pokrovsk region in south-east Ukraine. Almost a third of the total of 74 Russian attacks of the day were registered there.
All attacks were repulsed, it was reported. "Our guys are holding their own," the generals in Kiev announced.
Ukraine has been fending off a large-scale Russian invasion for more than two years. The border region of Belgorod serves as a deployment area and logistics base for Russian troops. The eastern Ukrainian city of Kharkiv is also attacked from there.
On the Ukrainian side, three people were killed by Russian artillery fire in the village of Ulakly in the eastern Donetsk region on Saturday. Five people were injured, Governor Vadym Filashkin wrote on Telegram. The village is located around 30 kilometres from the current front line.