Witkoff is expected to travel to Moscow next week with other senior US officials for talks with Russian leaders about a possible plan to end the nearly four-year-old war in Ukraine, the deadliest in Europe since World War II.
Ukrainian President Volodymyr Zelenskiy on Tuesday said he was ready to advance the US-backed framework for ending the war and to discuss disputed points with the US president in talks that he said should include European allies.
Kyiv and its European allies are worried that details of the plan leaked last week show it bows to key Russian demands - barring Ukraine's NATO entry, enshrining Russian control of one-fifth of Ukraine and limiting the size of Ukraine's army.
US policy toward the war in Ukraine has veered widely since the northern summer. Trump's hastily arranged Alaska summit with Russian President Vladimir Putin spurred worries that Washington was prepared to accept many Russian demands, but ultimately resulted in more US pressure on Russia.
The latest peace proposal caught many in Washington, Europe and Kyiv off guard, stirring anxiety that Trump might be willing to push Ukraine to sign a peace deal heavily tilted towards Moscow.
The plan - and the leaked Witkoff call - prompted unusually harsh criticism from Trump's fellow Republicans, who have generally marched in lockstep with the president since he began his second term.
Trump later said progress was being made and Moscow was making concessions even though the war - in which Russian forces have been advancing - was only going to move "in one direction."
But, while welcoming the Trump administration's efforts, Russian Deputy Foreign Minister Sergei Ryabkov told reporters in Moscow on Wednesday: "There can be no question of any concessions, or any surrender of our approaches to those key points."
Moscow also raised concerns about the leak to Bloomberg News of the transcript of a call between Witkoff and Putin's foreign policy aide, Yuri Ushakov, in which the US envoy advised Ushakov on how to pitch a peace plan to Trump.
Trump, on Air Force One, brushed aside a question from a reporter about why Witkoff appeared to be coaching Russian officials as "what a dealmaker does" and "a very standard form of negotiation." But Russia said the leak was an unacceptable attempt to undermine peace efforts and amounted to hybrid warfare.
Ushakov said he had used WhatsApp to speak to Witkoff on several occasions and the Russian newspaper Kommersant, which interviewed Ushakov, ran a story headlined: "Who set up Steve Witkoff?"
Bloomberg said it had reviewed a recording of the call. It was not clear how Bloomberg got the recording.
A Bloomberg News spokesperson said: "We stand by our story."
Trump on Tuesday said Witkoff would meet Putin and that Jared Kushner, who helped negotiate the deal that brought about an uneasy ceasefire in the Gaza war between Israel and the Palestinian militant group Hamas, would also be involved.
"As for Witkoff, I can say that a preliminary agreement has been reached that he will come to Moscow next week," Ushakov told reporters.
Asked by reporters whether a peace deal was close, Kremlin spokesman Dmitry Peskov was quoted by Russian news agency Interfax as saying: "Wait, it's premature to say that yet."
Russian forces control more than 19 per cent of Ukraine following Moscow's 2022 invasion, and have advanced in 2025 at the fastest pace since 2022, although the advances remain slow and Kyiv says Russia has incurred heavy losses to achieve them.