Several buildings were attacked in the western Russian region of Kursk on the border with Ukraine, Kursk Governor Roman Starovoyt announced. This could not be independently verified.
Seven civilians were killed in Ukraine's eastern Donetsk region by Russian troops, the head of the local military administration said.
At least 382 civilians have been killed and 1,096 injured in Donetsk alone since Russia's invasion, according to Ukrainian figures.
Russia's Deputy Prime Minister Marat Khusnullin visited Ukraine's Kherson on Tuesday, and said the region would take a "worthy place in our Russian family," RIA Novosti reported.