US envoy Steve Witkoff on Thursday said "a lot of progress" had been made in Ukraine peace talks and that negotiations were down to one last issue.
The United States has held talks with Russia, and separately with Kyiv and European leaders, on various different drafts of a plan for ending the war in Ukraine, but no deal has yet been reached despite Trump's repeated promises to clinch one.
"If both sides want to solve this, we're going to get it solved," Witkoff told an audience at the World Economic Forum in Davos.
"I think we've made a lot of progress," he added.
US President Donald Trump, a day earlier, told the Davos forum that the leaders of Russia and Ukraine would be "stupid" if they failed to come together and get a deal done.
Witkoff said he was headed to Moscow later in the day. He spoke in an impromptu appearance a breakfast meeting on the future of Ukraine, with panelists including NATO Secretary Mark Rutte and Finnish President Alexander Stubb.
Rutte expressed confidence that Trump was committed to Ukrainian independence and sovereignty. "I have never doubted this," Rutte said.
"What we need is to keep our eyes on the ball of Ukraine. Let's not drop that ball," he added.
Putin says he will meet US envoys Witkoff, Kushner
Additionally, Russian President Vladimir Putin said on Wednesday he would meet on Thursday with US envoys Steve Witkoff and Jared Kushner, who have been tasked with finding a solution to Russia's nearly four-year-old war with Ukraine.
Putin, quoted by Russian news agencies, said during a meeting of Russia's Security Council that he would discuss the possible use of frozen Russian assets with the US envoys in connection with recovery work in regions affected by the war.
"This possibility is also under discussion with representatives of the US administration," Russian news agencies quoted him as saying.