The governor of the western Russian region bordering Ukraine says members of a Ukrainian sabotage group had entered the Russian territory.
Belgorod region governor Vyacheslav Gladkov on Monday said counter-terrorism measures were taken to drive them away.
He added that eight people in the region were wounded by shelling.
Russian media meanwhile reported that 39 saboteurs had been killed by authorities.
Kremlin spokesperson Dmitry Peskov on Monday said Russian President Vladimir Putin had been informed of the incident.
Peskov said the Defense Ministry, the Federal Security Service, or FSB, and other security forces are trying to drive out the saboteurs or eliminate them.
Ukrainian presidential adviser Mykhailo Podolyak tweeted, "Ukraine is watching the events in the Belgorod region of Russia with interest and studying the situation, but it has nothing to do with it."
He suggested that underground guerrilla groups, which are composed of anti-Putin Russians, may be responsible for the incident.
Russian militias fighting for Ukraine have announced on social media that they will enter Russian territory and posted videos of military vehicles.