High-stakes US-Russia talks on ending the war in Ukraine failed to yield a breakthrough on Tuesday, as the Kremlin said "no compromise" had been found yet on the key question of territory.

Russian President Vladimir Putin met US President Donald Trump's son-in-law Jared Kushner and special envoy Steve Witkoff in the Kremlin, after earlier signalling that his forces were ready to fight on to achieve Russia's initial war goals.

The meeting is a crucial moment for Ukraine in what could be a fraught week following days of frantic diplomacy.

At the heart of it is a US plan to bring peace, which has since been revised under pressure from Kyiv and its European backers.

On occupied Ukrainian territories, "so far we haven't found a compromise, but some American solutions can be discussed," top Russian presidential aide Yuri Ushakov said after the meeting in the Kremlin.

"Some proposed formulations do not fit us, and work will continue," he added.

Trump said progress on ending the nearly four-year-long war would not be easy.

"Our people are over in Russia right now to see if we can get it settled," he said during a cabinet meeting at the White House. "Not an easy situation, let me tell you. What a mess."

Ukrainian President Volodymyr Zelensky said on Monday that any plan must end the war for good, and not just lead to a pause in the fighting that began with Moscow's offensive in February 2022.

He also said in a social media post that "there will be no simple solutions".

"What matters is that everything is fair and transparent. That there are no games played behind Ukraine's back. That nothing is decided without Ukraine – about us, about our future," he said.

Kushner and Witkoff were to present Putin with the new version of the US plan, which has been hammered out after the initial version raised fears in Kyiv and elsewhere in Europe that it made too many concessions to Moscow.

Ushakov said the initial US plan was broken down into four parts, which were discussed during the five-hour meeting in the Kremlin.

"There were some points we could agree on," the top Putin diplomatic aide said, but "the president did not hide our critical, even negative, stance on a number of proposals".

Putin has demanded that Kyiv surrender territory Moscow claims as its own.

The Kremlin also rejects any European force in Ukraine to monitor a truce.

In his social media post, Zelensky said "the most difficult questions are about territories, about frozen (Russian) assets... And about security guarantees."

Still, the talks in Moscow were "useful", Ushakov said, and Russia and US positions did not become farther apart after it. (AFP)