It was the latest twist in Trump's stop-and-go effort to resolve the war in Ukraine.
The decision to hold off on the meeting in Budapest which Trump had announced last week, was made following a call between Secretary of State Marco Rubio and Russian Foreign Minister Sergey Lavrov.
"I don't want to have a wasted meeting," Trump said. "I don't want to have a waste of time - so we'll see what happens."
Trump's hesitancy will likely come as a relief to European leaders, who have accused Putin of stalling for time with diplomacy while trying to gain ground on the battlefield.
The US and Russian presidents last met in Alaska in August, but the encounter did not advance Trump's stalled attempts to end a war that began almost four years ago.
The Kremlin didn't seem to be in a rush to get Trump and Putin together again either. Spokesperson Dmitry Peskov said "preparation is needed, serious preparation" before a meeting.
"Listen, we have an understanding of the presidents but we cannot postpone what has not been finalised," Peskov said.
On Wednesday, Trump will hold talks with NATO Secretary General Mark Rutte, according to a White House official who was not authorised to comment publicly. The official did not provide any detail about Trump's agenda for the talks.
The military alliance has been co-ordinating deliveries of weapons to Ukraine, many of them purchased from the US by Canada and European countries. A meeting of the Coalition of the Willing - a group of 35 countries who support Ukraine - is due to take place in London on Friday.
Separately, European countries are working with Ukraine on a 12-point proposal to end Russia's war along current battle lines, Bloomberg News reported.
A peace board chaired by Trump would oversee the implementation of the proposed plan, the report said, citing people familiar with the matter.
European leaders called on the United States to hold firm in demanding an immediate ceasefire in Ukraine, with present battle lines to serve as the basis for any future talks.
The Russian government has long demanded that Ukraine agree to cede more territory before any ceasefire.
Under the proposal, Ukraine would receive security guarantees, funds to repair war damage and a pathway to rapidly join the European Union, the Bloomberg report said, adding that once Russia follows Ukraine in agreeing to a ceasefire and both sides commit to halting territorial advances, the proposals envisage the return of all deported children to Ukraine and the exchanges of prisoners.
Both sides would enter into negotiations on the governance of occupied territories, although neither European countries nor Ukraine will legally recognise any occupied land as Russian, the report added, citing sources.
Reuters could not immediately verify the Bloomberg report.
with AP and EFE
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