The offer of a 30-day ceasefire goes beyond Zelensky's proposal for a partial truce in the sky and at sea.

The Ukrainian president thanked Trump for "the constructiveness" of the talks in Jeddah.

In a video message, Zelensky said Russia had to "show its willingness to stop the war or continue the war".

"It is time for the full truth," he added.

The Kremlin has not yet publicly responded. It said earlier on Tuesday it would issue a statement after being briefed by Washington on the outcome of the talks.

But influential Russian lawmaker Kostantin Kosachev said that any potential agreements would be "on our terms, not American".Kosachev, chairman of the Federation Council's international affairs committee, said "real agreements are still being written... at the front", stressing that Russian troops were advancing in Ukraine.

Russia launched a full-scale invasion of Ukraine in February 2022. Moscow currently controls about 20% of Ukrainian territory.

At the White House, Trump told reporters he would speak with Russian President Vladimir Putin, who would "hopefully" agree to the proposal.

"It takes two to tango, as they say," Trump said, adding he hoped the deal would be agreed in the next few days.

"We have a big meeting with Russia tomorrow, and some great conversations hopefully will ensue."

He added that he was open to inviting Zelensky back to Washington.

Russian Foreign Ministry spokeswoman Maria Zakharova said Russia had not ruled out talks with US representatives in the next few days, according to Russia's state-owned news agency Tass.

Asked by a reporter if Trump and Zelensky's relationship was "back on track," Rubio said he hoped it was "peace" that was back on track.

"This is not Mean Girls, this is not some episode of some television show," he said.

"Today people will die in this war, they died yesterday and - sadly - unless there's a ceasefire, they will die tomorrow."

The US and Ukrainian teams met after overnight drone attacks killed at least three people near Moscow - which Russia said showed Ukraine had rejected using diplomacy to end the war.Trump and Zelensky have also agreed to finalise "as soon as possible" a critical minerals deal, the joint statement said.

Ukraine has offered to grant the US access to its rare earth mineral reserves in exchange for US security guarantees - but this was derailed by the White House row.

Rubio said the deal had not been the subject of Tuesday's talks, but had been negotiated with Ukrainian and US treasuries.

The US delegation in Jeddah also included US National Secuirty Adviser Mike Waltz.

The joint US-Ukraine statement said Kyiv had "reiterated" that Europe should be involved in any peace process.

The shift in America's approach to the war - which has included locking Europe out of talks - has prompted several emergency meetings between European leaders in recent

The EU Commission President Ursula von der Leyen said the bloc welcomed Tuesday's "positive development".

Achieving a swift end to the war in Ukraine has been a key pledge for the US president.

He has placed increasing pressure on Zelensky to accept a ceasefire, without offering the immediate security guarantees insisted upon by the Ukrainian president.

On Friday, Trump issued a rare threat of further sanctions against Moscow in a push for a deal. Russia is already heavily sanctioned by the US over the war.