The Russian military said air defence units had downed four Ukrainian missiles in the region and the regional governor said the strikes had damaged a high-rise apartment building and other buildings in an adjacent village.
Ukrainian forces remain in Russia's Kursk region five months after sending troops across the border although the Russian military says much of the territory lost in the invasion has been recaptured.
"These strikes disrupt the ability of the Russian Federation to conduct terrorism against innocent Ukrainian civilians," the Ukrainian military said in a statement via the Telegram messaging app.
Another post showed a video of what the military said was damage to a Russian base in Ivanivskoye, next to Maryino.
Reuters could not independently verify battlefield accounts from either side.
Kursk regional governor Alexander Khinshtein said the strike on Ivanovskoye had shattered windows in a multi-storey apartment building and in private homes.
Also damaged were a school, a pharmacy and a shop.
A video showed work under way to repair damage to a facade.Â
In an effort to stop the Russian counteroffensive, several small towns that serve as bases for the troops advancing from the Kremlin have been shelled in recent weeks.
The Ukrainian forces often used HIMARS rocket artillery from the United States.
In November, the Ukrainian army had already fired UK Storm Shadow missiles at a Russian command post in Maryino.
Ukraine has been defending itself against a Russian attack for almost three years.
with DPA
