US President Donald Trump said on Sunday that he could meet "very soon" with Vladimir Putin, adding he believes his Russian counterpart genuinely wants to stop fighting in Ukraine.

"No time set, but it could be very soon," Trump told reporters, hours after Secretary of State Marco Rubio sought to play down expectations of upcoming high-level talks in Riyadh on ending the war.

With Rubio set to lead a high-level American delegation at the discussions with Russian officials in Saudi Arabia's capital in the coming days, a flurry of diplomacy was taking place as the Ukraine war nears its third anniversary.

Trump, addressing reporters after a flight on Air Force One, said his team had been speaking "long and hard" with Russian officials, including his Middle East envoy Steve Witkoff whom the president said met with Putin for about three hours recently.

"I think he wants to stop fighting," Trump said of Putin.

Asked whether he believes Putin wants to seize the entirety of Ukraine, Trump said: "That was my question to him.

"If he's going to go on... that would have caused me a big problem," Trump added.

"I think he wants to end it, and they want to end it fast. Both of them," he said, adding "Zelensky wants to end it too."

Ukrainian President Volodymyr Zelensky meanwhile said Sunday he believed Russia was preparing to "wage war" against a weakened NATO should Trump dilute US support for the alliance.

Trump appeared to dismiss Zelensky's remarks, telling reporters he was "not even a little bit" concerned about the Ukrainian leader's messaging.

Rubio is set to lead a high-level US team to Riyadh, but it remains unclear whether there will be any Ukrainian participation. Rubio said he wasn't even sure who Moscow was sending. (AFP)