Three Ukraine-based Russian paramilitary groups say they have crossed into Russia and are now fighting government troops there.
The Freedom of Russia Legion (FRL) and Siberian Battalion (SB) posted videos purportedly showing their fighters in Russia's Belgorod and Kursk regions.
The FRL and an exiled Russian politician claimed two villages were now in control of "liberation forces".
Russia's defence ministry said the breakthrough attempts were thwarted.
It claimed more than 234 Ukrainian troops had been killed and several tanks had been destroyed.
According to Belgorod's regional governor, Vyacheslav Gladkov, one member of Russia's territorial defence forces was killed and 10 civilians were injured.