“We are at the end now, and I actually am optimistic,” Witkoff said at a Ukrainian event on the sidelines of the World Economic Forum (WEF) in Davos, Switzerland, noting that "a lot of progress" had been made in Russia-Ukraine peace talks.

Expressing that he met with Ukraine's delegation on Wednesday evening, Witkoff praised Kyiv's negotiating team and said they spent "a lot of time together" since talks in Geneva in November last year.

“I think we’ve got it down to one issue, and we have discussed iterations of that issue, and that means it’s solvable. So if both sides want to solve this, we’re going to get it solved,” Witkoff further said.

He added that he and US President Donald Trump’s son-in-law Jared Kushner will be heading to the Russian capital Moscow on Thursday evening, and will later head to Abu Dhabi without staying overnight, where working group meetings will be held.

Witkoff and Kushner are scheduled to meet with Russian President Vladimir Putin in Moscow.

On Wednesday, Witkoff told CNBC at the WEF that there had been "lots of progress in the last six to eight weeks" with regard to a settlement in Ukraine.

He said the Kremlin had requested the talks in Moscow, and that they hopefully will have "something good to announce soon."

Both Witkoff and Kushner have held multiple meetings with Putin, as well as Ukrainian delegations, aimed at ending the Russia-Ukraine war, which is set to enter its fifth year next month.

In remarks to journalists at a briefing later Thursday, Kremlin spokesman Dmitry Peskov said that Putin's meeting with the US envoys will "definitely be after 7-8 pm" local time (1600-1700GMT), after which Russian presidential aide Yuri Ushakov will brief journalists on its results.

"We would not like to comment on the current stage of the negotiations, especially in the run-up to Witkoff's arrival in Moscow and his meeting with Putin," Peskov added.