The Russian Ministry of Defense says that Ukraine has retaliated in Russia’s Kursk region.
As officials in Ukraine also suggested an operation was underway, Moscow said it faced an attack with artillery and air power.
Ukrainian forces entered the Kursk region in August, seizing part of it. Russian forces have pushed them back in some areas without managing to completely dislodge them.
Ukrainian President Volodymyr Zelensky has said that security guarantees to end the war will be effective only if the United States under the leadership of Donald Trump provides them.
During a podcast interview with Lex Friedman, Zelensky praised the incoming US president’s influence and suggested that Trump at least has the leverage to deter Russia’s ongoing offensive.
During his campaign, Trump promised to end the war quickly without giving details.
“Trump and I will come to an agreement and … offer strong security guarantees together with Europe, and then we can talk to the Russians,” Zelenskiy said.
According to the Russian Defense Ministry, a Ukrainian assault force consisting of two tanks, a military engineering vehicle and 12 armored fighting vehicles (AFVs) launched an attack near the village of Berdin at around 09:00 (06:00 GMT) on Sunday.
It said Russian forces retaliated, destroying two tanks, a military engineering vehicle and seven armored vehicles. The fight continued, he added.
Aerial video of an armored column moving through the snow-covered countryside in broad daylight and coming under fire, with vehicles colliding, Russian state news agency RIA reported.
The BBC was not immediately able to confirm the Russian footage or the claims.
Speaking earlier, the head of Ukraine’s presidential office, Andriy Yermak, said there was “good news from the Kursk region” and that Russia was “getting what it deserves”.
Andriy Kovalenko, Ukraine’s top anti-corruption official, said in one Telegram Post on Sunday: “The Russians in Kursk are in serious trouble because they were attacked from many directions and it took them by surprise.”
One Russian blogger, Yuri Podoliaka, suggested that the operation could be diverted, while another, Alexander Coates, did not rule out that the actual attack could be launched elsewhere.
Kiev’s forces are reportedly short of manpower and have been losing ground in recent months as Russian troops advance in eastern Ukraine.
It comes as Ukraine’s air force says Russia launched another drone attack on Ukraine overnight.
It said it shot down 61 drones in Kyiv, Poltava, Sumy, Kharkiv, Chernihiv, Cherkasy, Dnipropetrovsk, Zhytomyr and Khmelnytskyi regions.
The air force said there were no direct strikes, but a few houses were damaged by an intercepted drone in the Kharkiv region.
In November, Ukraine reported that its troops were engaged in fighting with North Korean troops in the Kursk region.
The alleged appearance of North Korean troops was in response to a surprise attack launched by Ukrainian troops across the border in August, which advanced 18 miles (30 km) into Russian territory.
Moscow evacuated around 200,000 people from areas along the border and President Vladimir Putin condemned the Ukrainian offensive as a “massive provocation”.
After a fortnight, the Ukrainian high command claimed control of more than 1,200 square kilometers of Russian territory and 93 villages.
Some of this territory has been regained by Russia.