Trump has repeatedly said he wants to end the conflict but his efforts so far, including a summit with Putin in Alaska in August and meetings with Ukrainian President Volodymyr Zelenskiy, have not yet brought peace.
Zelenskiy's government is trying to push back after the US presented a plan last month that endorsed many of Russia's main demands.
European powers then came up with a counter-proposal and at talks in Geneva, the United States and Ukraine said they had created an "updated and refined peace framework" to end the war.
"I am so pleased to see you," Putin told Witkoff and Kushner when they met on Tuesday.
"It is a magnificent city," Witkoff told Putin after earlier strolling with Kushner and the Russian leader's envoy Kirill Dmitriev on Red Square near the mausoleum of Soviet state founder Vladimir Lenin.
Dmitriev and Putin aide Yuri Ushakov were also at the Kremlin meeting, along with interpreters.
Just before the Kremlin meeting, Putin accused European countries of seeking to undermine Trump's peace efforts by making proposals that they knew were unacceptable to Russia.
"They are on the side of war," Putin said of the European powers.
"We can clearly see that all these changes are aimed at only one thing: to block the entire peace process altogether, to make such demands which are absolutely unacceptable to Russia."
"If Europe suddenly wants to start a war with us and starts it," Putin said, then it would end so swiftly that there would be no one left for Russia to negotiate with.
Putin threatened to sever Ukraine's access to the sea in response to drone attacks on tankers of Russia's "shadow fleet" in the Black Sea.
Ukrainian Foreign Minister Andrii Sybiha said Putin's remarks showed he was not ready to end the war.
Russian forces control more than 19 per cent of Ukraine, or 115,600 square km, up only one percentage point from two years ago, although they have advanced in 2025 at the fastest pace since 2022, according to pro-Ukrainian maps.
But nearly four years into the Ukraine war, Russia has failed to conquer Ukraine, a much smaller neighbour which has been supported by European powers and the United States.
Zelenskiy said on Tuesday he had some optimism around peace efforts due to the speed of the process and the United States' interest in finding a solution.
"A little bit optimism was in my words because of some speed of negotiations, and from the American side, their interest in it. It showed that America is not withdrawing now from any kind of diplomatic way of dialogue and it is good," Zelenskiy told an event during a visit to Dublin.
Putin has said the discussions so far are not about a draft agreement but about a set of proposals that he said last week "could be the basis for future agreements".
Putin has said he is ready to talk peace but that if Ukraine refuses an agreement, then Russia's forces will advance further and take more Ukrainian territory.
A Russian source said the US administration's attempts to secure peace represented the best chance to end the war since talks with Ukraine broke down shortly after Russia's February 2022 invasion.
Putin, in video footage released on the eve of Witkoff's visit, hailed what his commanders said was Russia's capture of the city of Pokrovsk in eastern Ukraine as an important victory after a prolonged campaign.
Ukraine's military told Reuters its forces were still holding the northern part of the city and had attacked Russian forces in southern Pokrovsk.
US officials have put the casualty toll in the war at more than 1.2 million killed or wounded.
Neither Ukraine nor Russia discloses its losses.
