Trump said on Thursday that Putin had agreed to refrain from firing on Kyiv and other Ukrainian cities for a week because of cold weather, but did not say when that period would expire.
Kremlin spokesman Dmitry Peskov, replying to reporters' questions on Friday, did not cite the weather as a factor.
"President Trump did indeed make a personal request to President Putin to refrain from striking Kyiv for a week until February 1 in order to create favourable conditions for negotiations," he said.
Asked to confirm that Putin had agreed, he said: "Yes of course, there was a personal request from President Trump."
But he refused to answer further questions about whether the agreement covered only energy infrastructure or all aerial strikes, and when the halt on strikes on Kyiv was supposed to start.
It was also not clear whether Peskov was using "Kyiv" to refer only to the capital city, where hundreds of apartments have been left without heat and power after Russian strikes during the war in Ukraine, or to denote the whole of the country.
Kyiv has said it will reciprocate if Moscow, which sent tens of thousands of troops into Ukraine in February 2022, forgoes strikes on Ukrainian energy infrastructure.
Ukraine, which has grappled with severe power shortages this winter, is forecast to enter a brutally cold stretch starting on Friday that is expected to last into next week.
Separately, President Volodymyr Zelenskiy said Ukraine would be willing to stop attacks on Russian targets as part of a limited ceasefire, provided Russia halts strikes on Ukrainian energy infrastructure.
"If Russia doesn't fire on our energy facilities, then we won't attack theirs," the president told journalists on Friday.
However, he said no such assurances had yet been received from Moscow.
According to Zelenskiy, the proposal for a limited ceasefire was put forward by Washington. He said there had been no direct contact between Kiev and Moscow on the matter.
The Ukrainian Air Force said on Friday morning that Russia had launched 111 drones at the country overnight, with 80 of them shot down. There were no immediate reports of strikes on energy sites.
The last air raid alert for Kiev, which has recently come under heavy Russian bombardment that knocked out power and heating, was issued on Wednesday.
Zelenskiy said further talks mediated by Washington between Russian and Ukrainian delegations in Abu Dhabi, in the United Arab Emirates, were expected on Sunday, though he cautioned that the date and venue could still change.
with AP and DPA
