Russia on Monday evacuated parts of another region next to Ukraine after Kyiv sharply increased military activity near the border just days after its biggest incursion into sovereign Russian territory since the start of the 2022 war.

Ukrainian forces rammed through the Russian border early on Tuesday and swept across some Western parts of Russia's Kursk region, a surprise attack that may be aimed at gaining leverage in possible ceasefire talks after the U.S. election.

Apparently caught by surprise, Russia by Sunday has stabilised the front in the Kursk region, though Ukraine had carved out a sliver of Russian territory where battled were continuing on Monday, according to Russian war bloggers.

In the neighbouring Belgorod region to the south, the regional governor, Vyacheslav Gladkov, said that evacuations had begun from the Krasnaya Yaruga District due to "enemy activity on the border" that was a "threat".

"I am sure that our servicemen will do everything to cope with the threat that has arisen," Gladkov said. "We are starting to move people who live in the Krasnaya Yaruga district to safer places."

Russia has imposed a sweeping security regime in the Kursk, Bryansk and Belgorod regions while Russian ally Belarus said it was bolstering its troop numbers at its border after Minsk said Ukraine had violated its airspace with drones.

The audacious Ukrainian attacks on Russian sovereign territory are aimed at showing its Western supporters that Kyiv can still muster major military operations while trying to gain an bargaining chip ahead of possible ceasefire talks.

Russian forces, which have a vast numerical supremacy and control 18% of Ukrainian territory, have been advancing this year along the 1,000-km (620-mile) front after the failure of Ukraine's 2023 counteroffensive to make any major gains.

Ukraine broke its silence on the attacks on Saturday when President Volodymyr Zelenskiy said that Ukraine had launched an incursion into Russian territory to "restore justice" and pressure Moscow's forces.