"We have had very good and productive discussions with President Vladimir Putin and Russia yesterday, and there is a good chance that this terrible, bloody war will end", writes Trump on Truth Social.
But thousands of Ukrainian soldiers are surrounded by Russian military, he continues.
"I have strongly urged to spare their lives", writes Trump.
In a TV broadcast comment, Putin responds by urging the Ukrainian forces in Kursk to lay down their arms and surrender. Their lives will then be spared and they will be treated with dignity, claims Putin.
Ukraine's army simultaneously rejects Trump's claims about the situation for the Ukrainian forces in Kursk.
"There is no threat of our forces being surrounded", writes the general staff in a statement on social media according to AFP.
Zelenskyj: Sabotage
Ukraine's President Volodymyr Zelenskyj accuses in a post on X Vladimir Putin of sabotaging the diplomatic efforts towards a ceasefire, by setting "extremely difficult and unacceptable conditions from the start".
Russia's state media reports that Putin met with envoy Witkoff late on Thursday evening and that Putin then gave the American envoy information and "signals" intended for USA's President Donald Trump.
From the Kremlin's side, a "cautious optimism" is expressed regarding continued talks about a ceasefire in Ukraine. Putin said on Thursday that he was ready to talk about such a thing, although with great reservations. He also expressed a clear desire to talk to Donald Trump personally.
Behind the Scenes
Witkoff arrived in Moscow on Thursday and left the Russian capital early on Friday, according to a report from the state-controlled news agency Tass.
On Thursday, Putin appeared before a gathered press corps together with Belarus leader Aleksandr Lukasjenko, who is also visiting Moscow. It was then that the Russian president said he was open to a "peaceful solution" to the large-scale invasion war in Ukraine that he started in February 2022, but only if "the underlying fundamental problems" are removed.
The meeting with Witkoff did not take place in public, no pictures of them together have emerged, and the meeting was not announced until Witkoff had left.
On Thursday, Putin also spoke by phone with Saudi Arabia's Crown Prince and de facto leader Mohammed bin Salman, reports among others AFP.