The governor of Russia's Belgorod region said on Monday that a Ukrainian "sabotage group" had entered Russian territory in the Graivoron district bordering Ukraine and was being repelled by Russian forces.
However, the Ukrainian outlet Hromadske cited Ukrainian military intelligence as saying two armed Russian opposition groups, the Liberty of Russia Legion and the Russian Volunteer Corps (RVC), both consisting of Russian citizens, were carrying out the attack.
The Telegram channel Baza, which has links to Russia's security services, published aerial footage apparently showing a Ukrainian armored vehicle advancing on the Graivoron border checkpoint.
However, reports dried up late in the day as the governor, Vyacheslav Gladkov, imposed a special regime allowing authorities to clamp down on movement and communications.
Kremlin spokesman Dmitry Peskov said President Vladimir Putin had been informed, and that work was under way to drive out the "saboteurs", the state-run RIA Novosti news agency reported.
Gladkov said on Telegram that the Russian army, border guards, presidential guard and the FSB security service were involved in the operation. He said at least eight people had been wounded and three houses and an administrative building damaged.
Later, in a briefing streamed on social media, he said a large part of the local population had left, either in buses or their own vehicles, and that he had imposed a "counter-terrorist operation" regime.
This gives the authorities broad powers to limit activities and movement and, notably, to suspend or restrict communication services including mobile networks and the internet.
Baza said there were indications of fighting in three settlements along the main road leading into Russia. The "Open Belgorod" Telegram channel said power and water had been cut off to several villages.
Reuters was unable to verify the reports.
A group calling itself the Liberty of Russia Legion - a Ukraine-based Russian militia led by Russian opposition figure Ilya Ponomarev that says it is working inside Russia for Putin's overthrow - said on Twitter it had "completely liberated" the border town of Kozinka. It said forward units had reached the district center of Graivoron, further east.
"Moving on. Russia will be free!" it wrote.
Reuters