Russian forces prevented crossborder incursions from Ukraine on Tuesday and forced the attackers to retreat with significant losses, Russia's defense ministry said in a statement.
Earlier, at least two Ukraine-based armed groups purporting to be made up of Russians opposed to the Kremlin said they launched an incursion across Russia's western border.
Reuters could not independently verify either side's version of events.
The Russian defense ministry said the attacks took place around 3 a.m. Moscow time (0000 GMT) and used tanks and armored personnel carriers to target several locations on the Russian side of the border. It said Russian troops used missiles, artillery and air forces to repel the attacks.