Russia on Tuesday called on Ukrainian forces to "immediately" lay down arms and issued a new ultimatum for the defenders of the besieged port city of Mariupol to give up their resistance.

The Russian defence ministry's warning came after Ukrainian President Volodymyr Zelensky announced late on Monday the start of a new offensive by Moscow, focused on the east of the former Soviet state.

"We once again call on the Kyiv authorities to show reason and give the corresponding orders to fighters to cease their senseless resistance," the Russian defence ministry said in a statement.

"But, understanding that they will not get such instructions and orders from the Kyiv authorities, we call on (the fighters) to voluntarily take this decision and to lay down their arms."

The statement made no direct mention of a new ground offensive in eastern Ukraine.

But it warned that Moscow had "real-time proof about terrible new crimes being prepared by the Kyiv regime".

The defence ministry added that Ukrainian fighters resisting the advancing Russian forces in the Sea of Azov port of Mariupol were in a "catastrophic situation".

"The Russian armed forces once again offer the nationalist battalions and foreign mercenaries a chance to stop all military activity and to lay down their arms, starting at noon," it said.

"Everyone who lays down their arms will be guaranteed survival."