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.
Ukrainian President Volodymyr Zelensky said the Kursk operation, launched with a mass incursion in August, had established a buffer zone which prevents Russian forces from being deployed in key areas of the front in eastern Ukraine.
He said Russia had lost more than 38,000 soldiers in Kursk - nearly 15,000 of whom were unable to return to the front. It is not clear on whether he meant that they had been killed or severely injured.