The Kremlin said that Putin accepted some US proposals aimed at ending the war in Ukraine and was prepared to keep working to find a compromise.
US special envoy Steve Witkoff and Trump adviser and son-in-law Jared Kushner spent hours at the Kremlin, departing in the early hours of Wednesday with no specific breakthrough on ending the war.
Trump, speaking to reporters in the Oval Office, said Witkoff and Kushner briefed him about the talks via telephone and told him their impression from Putin was that "he would like to make a deal."
What happens now, however, is unclear, Trump said.
"What comes out of that meeting I can't tell you because it does take two to tango," Trump said, without elaborating.
He added: "We have something pretty well worked out (with Ukraine)".
A White House official said Witkoff and Kushner would meet with Ukrainian officials in Miami on Thursday.
Kremlin spokesman Dmitry Peskov, asked if it would be correct to say that Putin had rejected the US proposals, disagreed.
"A direct exchange of views took place yesterday for the first time," Peskov said.
"Some things were accepted, some things were marked as unacceptable. This is a normal working process of finding a compromise."
A Kremlin aide said after the meeting that "compromises have not yet been found."
Ukraine President Volodymyr Zelenskiy said in his nightly video address that his team is preparing for meetings in the United States and that the dialogue with Trump's representatives will continue.
"Only by taking Ukraine's interests into account is a dignified peace possible," he said.
Ukraine and its European allies accused Putin of feigning interest in peace efforts.
The Russian leader "should end the bluster and the bloodshed and be ready to come to the table and to support a just and lasting peace," UK Foreign Secretary Yvette Cooper said.
Ukrainian Foreign Minister Andrii Sybiha urged Putin to "stop wasting the world's time".
The remarks reflected the high tensions and gaping gulf that remain between Russia on one side and Ukraine and its European allies on the other over how to end a war that the Kremlin started when it invaded its neighbour nearly four years ago.
On the battlefront, Ukraine hit the Druzhba oil pipeline in Russia's central Tambov region, a source in Ukraine's GUR military intelligence says.
It was the fifth Ukrainian attack on the pipeline which supplies Russian oil to Hungary and Slovakia, according to Reuters calculations.
Hungary and Slovakia continue to buy energy supplies from Russia, even after other European Union countries cut ties following its invasion of Ukraine in 2022.
Ukrainian media said remote-controlled explosives were used in the attack.
Slovak pipeline operator and Hungarian oil and gas company said later on Wednesday that oil supplies through Druzhba were running as normal.
Ukraine attacked the pipeline once in March, twice in August and once in September this year.
with AP and DPA