Fierce fighting is under way for a second day in Russia's Kursk region after Ukraine launched a counter-attack on Sunday.
Moscow said it had met the attack with artillery and air power, and on Monday stated that Russian troops thwarted a breakthrough attempt by Ukraine.
The BBC was not immediately able to verify the Russian claims. Ukraine has not yet officially commented on its operations in Kursk.
However, on Sunday the head of Ukraine's presidential office, Andriy Yermak, said there "was good news from Kursk Region" and that Russia was "getting what it deserves".
Ukrainian forces entered the region of Kursk in August, seizing a chunk of territory. Russian forces have pushed them back in some areas without managing to eject them entirely.
According to the Russian defence ministry, a Ukrainian assault detachment consisting of two tanks, one military engineering vehicle and 12 armoured fighting vehicles (AFVs) attacked near the village of Berdin around 09:00 (06:00 GMT) on Sunday.
Russian forces hit back, it said, destroying both tanks, the military engineering vehicle and seven armoured fighting vehicles. Fighting continued, it added.
Aerial video of a column of armour moving through snow-covered countryside in daylight and coming under fire, with vehicles taking hits, was published by Russian state news agency Ria.
Ukraine's top counter-disinformation official Andriy Kovalenko said in a Telegram post: "The Russians in Kursk are experiencing great anxiety because they were attacked from several directions and it came as a surprise to them."
Oner Russian blogger, Yury Podolyaka, suggested the operation might have been diversionary, while another, Alexander Kots, did not rule out that the main attack could be launched somewhere else.
Kyiv's forces are reportedly suffering from manpower shortages and have been losing ground in the east of Ukraine in recent months, as Russian troops advance.
In November, Ukraine reported its troops had engaged in combat with North Korean troops in the Kursk region.
The reported appearance of North Korean soldiers was in response to a surprise attack launched across the border by Ukrainian troops in August, advancing up to 18 miles (30km) into Russian land.
Moscow evacuated almost 200,000 people from areas along the border and President Vladimir Putin condemned the Ukrainian offensive as a "major provocation".
After a fortnight, Ukraine's top commander claimed to control more than 1,200 sq km of Russian territory and 93 villages.
Some of that territory has been regained by Russia.
At the weekend, Ukrainian President Volodymyr Zelensky said that security guarantees leading to an end to the war would only be effective if the US under Donald Trump provided them.
During a podcast interview with Lex Fridman, Zelensky praised the incoming US president's influence and suggested Trump had the leverage to at least halt Russia's continued invasion.
Trump pledged during his election campaign to end the war quickly, without giving details.
Zelensky said "Trump and I will come to an agreement and... offer strong security guarantees, together with Europe, and then we can talk to the Russians".
But on Monday, French President Emmanuel Macron said that Ukraine needed to have a "realistic" position on territorial issues and warned there would be no "quick and easy" solution to the conflict.