The Russian military said on Tuesday it had pushed Ukrainian forces out of a settlement called Guyevo in Russia's Kursk region and had carried out air and artillery strikes on Ukrainian troops across the border.

Russia has been trying since August last year to eject Ukrainian forces from Kursk after Kyiv's troops mounted a surprise incursion that embarrassed President Vladimir Putin and which Ukrainian President Volodymyr Zelenskyy hoped would give him a bargaining chip in any future talks.

But Russia has retaken a swath of territory inside Kursk in recent months, pushing the Ukrainians closer towards the border. It has also begun to take territory in Ukraine's neighboring Sumy region after Putin spoke of the possibility of carving out a buffer zone.

On Tuesday, Russia's Defence Ministry said it had retaken the settlement of Guyevo.

"The armed forces of the Russian Federation continue to crush the Ukrainian army formations on the territory of Kursk region," the ministry said in a statement.

It said its forces had also defeated Ukrainian troops in fighting around two other settlements.

Reuters could not verify the battlefield claims.

Ukraine's authoritative DeepState war map shows Ukraine in control of about 58 square kilometers (22 square miles) of Russian territory in Kursk, down from as much as 1,400 square kilometers claimed by Kyiv last year.

Ukrainian President Volodymyr Zelenskyy confirmed for the first time on Monday that Ukrainian troops have also been active in Russia's adjacent Belgorod region.

Russian commander Apti Alaudinov was quoted by the state RIA news agency as saying on Friday that the situation in the Belgorod region was "under control" after the Ukrainian army tried to break through the border around two weeks ago.