Volodymyr Zelensky will meet Donald Trump on Monday for crunch talks on the war in Ukraine in the wake of the U.S. president's historic summit with Vladimir Putin in Alaska last week.

Trump heralded 'great progress' with his Russian counterpart as they emerged from their face-to-face meeting on Friday, but the exact details of what was said has remained closely guarded ahead of Monday's meeting in Washington.

Sources familiar with the talks said that Putin demanded Ukraine withdraw from Donetsk and Luhansk, industrial oblasts straddling the Donbas region. Russia would then agree to freeze battle lines as they lay. Zelensky was said to have rejected the demands.

As the Russian advance continues, Putin's designs on Ukraine have hardened, not relaxed. Trump on Sunday shrugged that Zelensky should also accept Russia's illegal 2014 annexation of Crimea.

Zelensky maintains that Ukraine cannot concede land without amending its constitution via referendum, and urges that any ceasefire must be premised on security guarantees from allies - citing dozens of historical breaches by Russia.