US President Donald Trump says Russia and Ukraine will "immediately" start negotiating towards a ceasefire and an end to the war, after a two-hour phone call with Russian counterpart Vladimir Putin.

Trump, who described the conversation as having gone "very well", also said conditions for peace would need to be negotiated between the two parties.

Despite the note of optimism from Trump, who also spoke with Ukrainian President Volodymyr Zelensky, any ceasefire or peace deal does not appear close.

Putin said he was ready to work with Ukraine on a "memorandum on a possible future peace agreement", while Zelensky said "this is a defining moment", and urged the US not to distance itself from talks.

In his remarks, the Russian president did not address demands from the US and European countries for an unconditional 30-day ceasefire.

After his one-on-one call with Trump, Zelensky reaffirmed Ukraine's desire for a "full and unconditional ceasefire", and warned if Moscow is not ready, "there must be stronger sanctions".

Speaking earlier before Trump's conversation with Putin, Zelensky said he had asked that any decisions about Ukraine were not made without his country, calling them "matters of principles" for Ukraine.

He added he did not have any details on a "memorandum" but said once they have received anything from the Russians, they will "be able to formulate their vision accordingly".

Writing on his Truth Social page after the call, Trump said: "Russia and Ukraine will immediately start negotiations toward a Ceasefire and, more importantly, an END to the War," adding he had informed Zelensky of this in a second call, which also included other world leaders.

He added: "The conditions for that will be negotiated between the two parties, as it can only be, because they know details of a negotiation that nobody else would be aware of."

Zelensky said the negotiation process "must involve both American and European representatives at the appropriate level".

"It is crucial for all of us that the United States does not distance itself from the talks and the pursuit of peace, because the only one who benefits from that is Putin," he explained.

Talking at a White House event later in the day, Trump said the US would not be stepping away from brokering talks between Russia and Ukraine, but that he has a "red line in his head" on when he will stop pushing on them both.

He also denied that the US was stepping back from its negotiating role.

In recent weeks, Trump has repeatedly warned that the US would step away from negotiations as he became increasingly frustrated at the lack of developments from both Moscow and Kyiv in the way of peace.

When asked on what he believes on Russia, he said he thinks Putin has had enough of the war and wants it to end.

Meanwhile, Putin - who described the call with Trump, which he took from a music school on a visit to the city of Sochi, as "frank, informative and constructive" - also spoke of the potential for a ceasefire.

"We have agreed with the US president that Russia will offer and is ready to work with Ukraine on a memorandum on a possible future peace agreement," he said.

This, he added would define "a number of positions" including "principles of the settlement and a timeline for concluding a possible peace agreement...including a possible ceasefire for a certain period of time, should relevant agreements be reached".

Yury Ushakov, an aide to the Russian president, said a ceasefire timeframe was not "discussed... although Trump, of course, emphasises his interest in reaching one or another agreement as soon as possible".

Zelensky held a second call with Trump after the US president spoke to Putin, which also included President of the European Commission Ursula von der Leyen, and the leaders of France, Italy, Germany and Finland.

"I want to thank President Trump for his tireless efforts to bring a ceasefire to Ukraine," von der Leyen said, adding: "It's important that the US stays engaged."

Italian Prime Minister Giorgia Meloni said Pope Leo's offer to host potential peace talks was a gesture welcomed by the US and the other leaders in the call, and "judged positively".

Earlier this month, the new Pope offered the Vatican as a venue for possible peace talks after Putin turned down Zelensky's offer to meet face-to-face in Turkey for negotiations.

Kyiv has previously said Putin's comments saying he desires peace are hollow.

"Putin wants war," Andriy Yermak, a top aide to the Ukrainian president, said after Russia on Sunday launched what Ukraine said was its biggest drone attack since the full-scale invasion began.

Ukraine says at least 10 people have been killed in Russian strikes in recent days - including nine people in an attack on a civilian minibus in north-eastern Ukraine. Russia says it has also intercepted Ukrainian drones.

The strike on the bus happened just hours after Russia and Ukraine held their first face-to-face talks in more than three years. A prisoner swap was agreed but there was no commitment to a ceasefire.

Trump had offered to attend the talks in Turkey if Putin would also be there, but the Russian president declined to go.

Russia has declared ceasefires before - but only temporary ones. It declared one for 8-11 May - which coincided with victory celebrations to mark the end of World War Two - but Kyiv would not sign up to it, saying Putin could not be trusted and that an immediate 30-day ceasefire was needed.

The Kremlin announced a similar, 30-hour truce over Easter, but while both sides reported a dip in fighting, they accused each other of hundreds of violations.

Russia and Ukraine have been at war since Moscow launched a full-scale invasion of Ukraine in February 2022.