Mystery surrounds the first direct contact between the leaders of the two largest nuclear powers since Russian began its full-scale war in Ukraine in February 2022, with both Washington and Moscow offering partial answers and hints.
Trump, speaking to reporters aboard Air Force One on Sunday, Â said he believed the United States was making progress, but declined to provide details about any communications with Putin.
Asked whether he had had a conversation with Putin since he became president on January 20 or before, Trump said: "I've had it. Let's just say I've had it...And I expect to have many more conversations. We have to get that war ended."
"If we are talking, I don't want to tell you about the conversations," Trump said.
Kremlin spokesman Dmitry Peskov, speaking to reporters in Moscow, repeated a statement from Sunday on whether or not there had been a Putin-Trump phone call: "There is nothing else I can say. I can neither confirm nor deny it."
Peskov on Sunday said "many different communications are emerging."
The conflict in eastern Ukraine began in 2014 after a Russia-friendly president was toppled in Ukraine's Maidan Revolution and Russia annexed Crimea, with Russian-backed separatist forces fighting Ukraine's armed forces.
Putin last spoke to former US president Joe Biden in February 2022, shortly before ordering troops into Ukraine.
Moscow now controls a chunk of Ukraine about the size of the American state of Virginia and is advancing at its fastest pace since the early months of 2022.
Trump, author of the 1987 book, Trump: the Art of the Deal, has repeatedly said he wants to end the war and that he will meet Putin to discuss it, though the date or venue for a summit is still not publicly known.
Saudi Arabia and the United Arab Emirates are seen by Russia as possible venues for a summit, Reuters reported earlier this month.
On June 14, Putin set out his opening terms for an immediate end to the war: Ukraine must drop its NATO ambitions and withdraw its troops from the entirety of the territory of four Ukrainian regions claimed and mostly controlled by Russia.
Reuters reported in November that Putin is open to discussing a Ukraine peace deal with Trump but rules out making any major territorial concessions and insists Kyiv abandon ambitions to join NATO.
Ukrainian President Volodymyr Zelenskiy told Reuters that he wanted Ukraine to supply the US with rare earths and other minerals in return for financial support for its war effort.
