US President Donald Trump says he plans to speak to his Russian counterpart Vladimir Putin on Tuesday about ending the war in Ukraine, adding discussions are already ongoing about "dividing up certain assets" between the warring parties.

US officials had expressed optimism on Sunday that a Ukraine-Russia ceasefire deal could be reached in weeks after Washington proposed a halt in fighting in the three-year war after talks in Saudi Arabia, which Kyiv accepted.

"I think we'll be talking about land... we'll be talking about power plants," Trump said aboard Air Force One.

"I think we have a lot of it already discussed very much by both sides, Ukraine and Russia. We're already talking about that, dividing up certain assets."

Washington and Kyiv's European allies are pressing Moscow to accept a halt in the fighting, but Putin has given no clear answer – instead listing a string of conditions and raising "serious questions" over the proposal.

Trump's envoy for the conflict, Steve Witkoff, who met for several hours with Putin days ago, told CNN that he thinks "the two presidents are going to have a really good and positive discussion this week".

Trump, he added, "really expects there to be some sort of deal in the coming weeks, maybe, and I believe that's the case".

Ukraine's Volodymyr Zelensky on Saturday accused the Kremlin of not wanting to end the war. He warned that Moscow wanted to first "improve their situation on the battlefield" before agreeing to any ceasefire. (AFP)