The governor of Russia's Belgorod region said on Monday that a Ukrainian army 'sabotage group' had entered Russian territory in the Graivoron district, which borders Ukraine.
The politician also stated that at least three people had been injured and three houses and a local administrative building damaged during a cross-border attack from Ukraine.
In a statement on Telegram, Vyacheslav Gladkov said that the Russian army, border guards, presidential guards and the FSB security service were taking measures to repel the incursion.
He said no civilians had been harmed, and that there was no evacuation underway.
Kremlin spokesman Dmitry Peskov said Russian President Vladimir Putin had been informed of the incursion, and that work was underway to drive the "saboteurs" out, the state-run RIA Novosti news agency reported.
Earlier, the Telegram channel Baza, which is linked to Russia's security services, had published footage apparently showing a Ukrainian armored vehicle advancing on the Graivoron border checkpoint.
Both Russian and Ukrainian officials refuse responsibility
It said there were indications of fighting in three settlements on the main road leading from Ukraine into Russia. The "Open Belgorod" Telegram channel said power and water had been cut off to several villages.
Ukrainian media cited Ukrainian military intelligence as saying the Liberty of Russia Legion and the Russian Volunteer Corps, both consisting of Russian citizens, were behind the attack.
A group calling itself the Liberty of Russia Legion, which claims to be planning attacks inside Russia, said on Twitter it had "completely liberated" the border town of Kozinka and its forward units had reached the district center of Graivoron further east.
"Moving on. Russia will be free!" it wrote.
Earlier on Monday, the group released a video showing five heavily armed fighters: "We are Russians, like you. We are people like you. We want our children to grow up in peace," one said facing the camera. "It is time to put an end to the dictatorship of the Kremlin."
Reuters was unable to verify the reports and the Ukrainian military was not immediately available for comment.