Russian President Vladimir Putin said on Thursday that he would end his Ukraine offensive if Kyiv withdrew from territory Moscow claims at its own – otherwise his army would take it by force.

The Russian army has been slowly but steadily grinding through eastern Ukraine in costly battles against outnumbered and outgunned Ukrainian forces.

Washington has meanwhile renewed its push to end the nearly four-year war, putting forward a surprise plan that it hopes to finalise through upcoming talks with Moscow and Kyiv.

"If Ukrainian forces leave the territories they hold, then we will stop combat operations," Putin said during a visit to Kyrgyzstan. "If they don't, then we will achieve it by military means."

Russia controls around one-fifth of Ukraine's territory. The issue of occupied land, which Kyiv has said it will never cede, is among the biggest stumbling blocks in the peace process.

Another important issue in the talks are Western security guarantees for Ukraine, which Kyiv says are needed to prevent Moscow from attacking again in the future.

Washington's original plan – drafted without input from Ukraine's European allies – would have seen Kyiv withdraw from its eastern Donetsk region and the United States recognise the Donetsk, Crimea and Lugansk regions as Russian.

The US pared back the original plan over the weekend following criticism from Kyiv and Europe, but has not yet released the new version.

Putin, who has seen the new plan, said it could be a negotiation starter.

"Overall, we agree that it could form the basis for future agreements," he said of the latest draft, which the United States is thought to have shortened to about 20 points. But Russia was still seeking international recognition of the occupied territories, Putin added.

Ukrainian President Volodymyr Zelensky's top aide, Andriy Yermak, strongly denied that in an interview with US outlet The Atlantic published on Thursday.

"As long as Zelensky is president, no one should count on us giving up territory. He will not sign away territory," Yermak said.

"All we can realistically talk about right now is really to define the line of contact," he said, referring to the sprawling 1,100 kilometre front line.

US negotiator Steve Witkoff was expected in Moscow next week to discuss the revised document, Putin said.

US Army Secretary Dan Driscoll is meanwhile due to visit Kyiv later this week, according to Yermak. (AFP)