Russian Foreign Minister Sergei Lavrov gave Ukraine an ultimatum on Monday to fulfil Moscow's proposals, including surrendering territory Russia controls, or its army would decide the issue, a day after President Vladimir Putin said he was open to talks.

Kyiv and its Western allies have dismissed Putin's offer to talk, with his forces battering Ukrainian towns with missiles and rockets and Moscow continuing to demand that Kyiv recognize its conquest of a fifth of the country.

"Our proposals for the demilitarization and denazification of the territories controlled by the regime, the elimination of threats to Russia's security emanating from there, including our new lands, are well known to the enemy," state news agency TASS quoted Lavrov as saying late on Monday.

"The point is simple: Fulfil them for your own good. Otherwise, the issue will be decided by the Russian army."