Donald Trump in the White House (Reuters: Evelyn Hockstein)
In short:
US President Donald Trump has said that the US and Vladimir Putin had "productive" discussions in Moscow and there was a "very good chance" the war in Ukraine can end.
Posting on Truth Social, he asked the Russian President to spare the lives of Ukrainian troops who he claimed were "completely surrounded".
What's next?
US envoy Steve Witkoff has been sent back to Washington with a series of demands from the Kremlin.
Ukraine has denied that its soldiers were encircled in Kursk and has said that Russia's list of conditions is evidence that Mr Putin does not want to end the conflict.
Donald Trump has said there is a "very good chance" the war between Russia and Ukraine can end after the US held "productive" discussions with Vladimir Putin on Thursday.
It comes after US envoy Steve Witkoff held talks with the Russian president in Moscow on Thursday and headed back to Washington with a list of conditions from the Kremlin.
Posting on Truth Social, the US President also called on Russia to spare the lives of thousands of Ukrainian troops, who he said were "completely surrounded" and in a "bad and vulnerable position".
Kyiv has denied that its soldiers are encircled in Kursk, Ukraine's only foothold into Russian territory, and has said that Mr Putin's series of conditions were proof that Russia wanted to prolong the conflict.
"We had very good and productive discussions with President Vladimir Putin of Russia yesterday, and there is a very good chance that this horrible, bloody war can finally come to an end" President Trump wrote in a Truth post.
He went on: "BUT, AT THIS VERY MOMENT, THOUSANDS OF UKRAINIAN TROOPS ARE 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."
Kyiv was quick to counter the assertion its forces were under pressure in Kursk.
“Reports of the alleged ‘encirclement’ of Ukrainian units by the enemy in the Kursk region are false and fabricated by the Russians for political manipulation and to exert pressure on Ukraine and its partners,” Ukraine’s general staff wrote in a statement.
Meanwhile, Volodymyr Zelenskyy sounded an optimistic note.
"Right now, we have a good chance to end this war quickly and secure peace. We have solid security understandings with our European partners," he said on X.
"There was a productive meeting with our American partners in Saudi Arabia."
But the Ukrainian president warned allies about trusting Mr Putin.
"Yesterday, we heard from Putin, he’s putting forward some conditions that clearly show he does not want any ceasefire. He needs war – this has always been obvious, and it is obvious now," he said.
"Putin is lying about the real situation on the battlefield, he is lying about the casualties, he is lying about the true state of his economy, which has been damaged by his foolish imperial ambitions, and he is doing everything possible to ensure that diplomacy fails."
Meanwhile, Mr Putin said on Friday that Russia will guarantee the safety of Ukrainian troops in the Kursk region if they surrender.
Rubio 'cautiously optimistic'
US Secretary of State Marco Rubio, at a G7 meeting in La Malbaie, Canada, said he was "cautiously optimistic" about the prospect of a ceasefire deal.
He said Mr Witkoff was returning to the United States and there may be discussions about Ukraine over the weekend.
"But we certainly feel like we're at least some steps closer to ending this war and bringing peace. But it's still a long journey," he told reporters.
NATO Secretary General Mark Rutte, who met Mr Trump on Thursday, told Fox News that Mr Trump's drive to get Russia to spare the lives of Ukrainian soldiers was "extremely helpful and extremely important."
The Trump administration launched its latest round of outreach to Moscow this week after Ukraine agreed in principle to a ceasefire at talks with US officials in Saudi Arabia.