Hours after a Russian regional governor said the attackers had been pushed back, the defence ministry issued a statement saying that fighting was still going on.
"Troops covering the state border, together with units of the border troops of the FSB (security service) of Russia, are repelling attacks and inflicting fire on the enemy in the area of the state border and on (Ukrainian) reserves in the Sumy region," the statement said.
It said Russia was using warplanes to strike Ukrainian armoured vehicles, and had moved its own reserves into the area of the fighting.
Ukraine's general staff, in a regular update on Tuesday, reported Russian strikes on border villages but did not mention any Ukrainian offensive operation at the border.
Russian regions near the border have come under frequent Ukrainian shelling in the course of the war in Ukraine as well as occasional incursions by groups of anti-Kremlin Russian volunteers who are fighting on Ukraine's side.
Russia said up to 300 Ukrainian fighters, backed by tanks, had taken part in the reported attack on Tuesday against Russian border units in Nikolayevo-Daryino and Oleshnya, two settlements in Russia's Kursk region.
Reuters could not independently verify battlefield accounts.
Alexei Smirnov, acting governor of the Kursk region, said Russian soldiers and FSB forces had repelled a Ukrainian attack but the situation at the border remained "difficult".
In a series of updates on social media, Smirnov said two Russian civilians had been killed, one by shelling and the other by a drone, and 18 others were wounded.
Russian media quoted the FSB as saying that Russian forces had dealt with an armed "provocation" by Ukraine.
Ukraine's main military effort is focused on fighting back Russian forces who control nearly a fifth of its territory after almost two-and-a-half years of war and have made a series of gradual gains in the past six months.
Позитивна щоденна бойова робота за будь-якої погоди розрахунку САУ «Богдана» 45 окремої артилерійської бригади Збройних Сил України по цілях російських окупантів-ворогів із негативним для останніх результатом. Східний напрямок. — Генеральний штаб ЗСУ (@GeneralStaffUA) pic.twitter.com/5gttr2vC6pAugust 5, 2024
Ukrainian strikes inside Russia's own territory have mostly involved shelling of border regions and drone attacks on targets such as oil refineries and fuel depots.
A Russian missile attack on the city of Kharkiv in northeastern Ukraine damaged a medical clinic and injured at least five people on Tuesday, the governor of the Kharkiv region said.
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