"At the suggestion of the American side, an agreement was essentially reached to hold a bilateral meeting at the highest level in the coming days, that is, a meeting between President Vladimir Putin and Donald Trump," Kremlin aide Yuri Ushakov said.
"We are now beginning concrete preparations together with our American colleagues," he added in televised comments.
Next week is the target date for a summit, Ushakov said, while noting that such events take time to organise.
The possible venue will be announced "a little later," he said.
A meeting between the two presidents would be their first since Mr Trump returned to office this year. And a face-to-face meeting would be the first between a sitting US and Russian president since Joe Biden met Putin in Geneva in June 2021, some eight months before Russia launched the biggest attack on a European nation since World War II.
Putin and Ukrainian President Volodymyr Zelenskiy have not met since December 2019 and make no secret of their contempt for each other.
The New York Times reported earlier that Trump told European leaders during a call on Wednesday, he intended to meet with Putin and then follow up with a trilateral involving the Russian leader and Zelenskiy.
White House press secretary Karoline Leavitt said: "The Russians expressed their desire to meet with President Trump, and the president is open to meeting with both President Putin and President Zelenskiy."
The details emerged following a meeting on Wednesday between Putin and US special envoy Steve Witkoff that Trump described as having achieved "great progress" in a Truth Social post, although later said he would not call it a breakthrough.
A Kremlin aide said the talks were "useful and constructive".
The diplomatic manoeuvres come two days before a deadline set by Trump for Russia to agree to peace in Ukraine or face new sanctions.
Trump has been increasingly frustrated with Putin over the lack of progress towards peace and has threatened to impose heavy tariffs on countries that buy Russian exports, including oil.
Trump on Wednesday also said he could announce further tariffs on China similar to the 25 per cent duties announced earlier on India over its purchases of Russian oil.
"We did it with India. We're doing it probably with a couple of others. One of them could be China," he said.
The White House official earlier said that while the meeting between Witkoff and Putin had gone well and Moscow was eager to continue engaging with the United States, secondary sanctions that Trump had threatened against nations doing business with Russia were still expected to be implemented on Friday.
Ushakov said the two sides had exchanged "signals" on the Ukraine issue and discussed the possibility of developing strategic co-operation between Moscow and Washington, but declined to give more details.
Zelenskiy said he believed pressure had worked on Russia and Moscow was now more "inclined" to a ceasefire.
"The pressure on them works. But the main thing is that they do not deceive us in the details - neither us nor the US," he said in his nightly address.
Trump on Truth Social said he had updated some of Washington's European allies following Witkoff's meeting.
A German government spokesperson said Trump provided information about the status of the talks with Russia during a call with the German chancellor and other European leaders.
Trump took a key step toward punitive measures on Wednesday when he imposed an additional 25 per cent tariff on imports from India, citing New Delhi's continued imports of Russian oil.
The Kremlin says threats to penalise countries that trade with Russia are illegal.
with DPA and AP
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