Speaking at the Valdai Discussion Club in the Black Sea resort town of Sochi, Putin called Trump a “courageous man” after a July assassination attempt.
Putin also said he was ready for dialogue and that Trump's campaign statements deserve attention.
His remarks came after a Kremlin spokesperson had said Wednesday there was no indication of Putin extending a congratulations to Trump following his electoral victory over Vice President Harris.
Trump has often praised Putin, calling him a "genius" after his 2022 invasion of Ukraine. He also reportedly called him seven times since leaving the White House in January 2021 and sent the Russian leader a COVID-19 test kit in 2020.
Veteran journalist Bob Woodward, who reported that Trump had called Putin after leaving office, pointed to their relationship as something to watch in the next four years.
"There is much to watch, particularly in that relationship," Woodward said.
Ukrainian President Volodymyr Zelensky congratulated Trump early Wednesday after it became clear he would win the election and the Ukrainian leader later spoke to Trump by phone.
Zelensky has so far offered an upbeat tone about the prospect of a second Trump administration.
In a speech in Budapest on Thursday, Zelensky described the phone call with Trump as "productive" and "good."
"Of course, we cannot yet know what his actions will be. But we do hope that America will become stronger," he said, saying this was "the kind of America that Europe needs."
But Zelensky also said it was vital for allies to stand by Ukraine and not offer concessions, specifically referring to European nations, and that Kyiv must decide what peace looks like with Russia.
"It is up to Ukraine to decide what should and should not be on the agenda for ending this war,” he said.
A second Trump administration is expected to upend U.S. national security and foreign policy, throwing into doubt Washington's support for Ukraine and other European allies.
Trump has pledged to end the war in Ukraine by the time he takes office on Jan. 20, though he has not offered details on how, spurring fears he will cede territory to Russia in return for a fragile peace.
And Trump also threatened to let Russia do "whatever the hell they want" to European members of NATO who don't pay enough in defense spending.
