US President Donald Trump said he had a "lengthy and highly productive" call with Russian President Vladimir Putin on Wednesday in which they agreed to "immediately" start negotiations to end the Ukraine war.

Trump said on Truth Social that both leaders had extended invitations of "visiting each other's nations," while the US leader said he would be calling Ukrainian President Volodymyr Zelensky "right now" to inform him about the call.

In an extraordinary thaw in relations between Washington and Moscow, the Kremlin separately said the call lasted one and a half hours and that Putin and Trump had agreed that the "time has come to work together."

Putin also told Trump that a "long-term settlement" of the Ukraine conflict sparked by Russia's 2022 invasion of its pro-Western neighbor was possible, and invited the US president to Moscow, the Kremlin said.

The Trump-Putin call came after a prisoner swap this week that saw Moscow free US teacher Marc Fogel while Washington released Russian cryptocurrency kingpin Alexander Vinnik.

Trump heaped praise on the Russian president in his Truth Social post, saying that Putin "even used my very strong Campaign motto of, 'COMMON SENSE.'"

He said they "both agreed, we want to stop the millions of deaths taking place in the War with Russia/Ukraine" — with Trump using an unconfirmed figure for the toll in the war.

"We agreed to work together, very closely, including visiting each other’s Nations," said Trump.

"We have also agreed to have our respective teams start negotiations immediately, and we will begin by calling President Zelensky, of Ukraine, to inform him of the conversation, something which I will be doing right now."

Trump said he had asked US Secretary of State Marco Rubio, CIA Director John Ratcliffe, National Security Advisor Michael Waltz and his Middle East envoy Steve Witkoff "to lead the negotiations which, I feel strongly, will be successful."