Moscow, Russia - Russian President Vladimir Putin on Friday called on Ukrainian troops fighting in the Kursk region to surrender, after US President Donald Trump urged him to "spare" the lives of Ukrainian soldiers.

Trump and Putin said that the Russian army had Ukrainian forces surrounded there – claims rejected by Kyiv, even as President Volodymyr Zelensky conceded that his forces were coming under increasing pressure.

Russia has mounted a rapid counteroffensive over the last week, recapturing swathes of land and settlements in the western border region from Ukraine.

"We are sympathetic to President Trump's call," Putin said in televised remarks.

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"If they lay down their arms and surrender, they will be guaranteed life and dignified treatment," he added.

"In order to effectively implement the US president's call, [there needs to be] a corresponding order from Ukraine's military-political leadership to its military to lay down their arms and surrender," Putin added.

In a post on his Truth Social platform, Trump had appealed to Putin over what he said were "thousands" of Ukrainian troops "completely surrounded by the Russian military, and in a very bad and vulnerable position".

"I have strongly requested to President Putin that their lives be spared. This would be a horrible massacre, one not seen since World War II," he said.

Moscow has recaptured the vast majority of territory Kyiv seized in its cross-border assault into Kursk last August, including in a rapid counteroffensive over the last week.

Ukraine denied Trump's and Putin's claims and said it was holding on to territory there.

"There is no threat of our units being encircled," the General Staff wrote in a statement on social media.

But Zelensky admitted his troops were under intense Russian pressure.

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"The situation in the Kursk region is obviously very difficult," Zelensky told reporters in Kyiv.

He said, however, that Ukraine's offensive there had forced Russia to pull its troops from other embattled areas of the front, easing pressure on Ukrainian troops fighting to keep control of the eastern logistics hub of Pokrovsk.

"I think the situation in the Pokrovsk sector is now stable, and it will be very difficult to find an opportunity to occupy Pokrovsk again," Zelensky said.