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.

The Russian defence ministry's warning came after Ukrainian President Volodymyr Zelensky announced late on Monday the start of a new offensive by Moscow that is 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 Russian Defence Minister Sergei Shoigu confirmed that his forces were "gradually implementing our plan to liberate" eastern Ukraine.

"We are taking measures to restore peaceful life," he said in a televised meeting with Russian military commanders.

Some of the heaviest fighting of the Russian campaign has focused around the strategic Sea of Azov port city of Mariupol.

The port offers a land bridge between Moscow-controlled parts of eastern Ukraine and the Kremlin-annexed peninsula of Crimea.

The Russian defence ministry said Ukrainian forces still holed up inside the devastated city's main metallurgical plant were facing 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," the Russian ministry said.

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

But Donetsk rebel commander Eduard Basurin said separatist "shock troops" had already launched an assault on the plant.

"The Russian Federation is really helping us with this, providing aerial and artillery support," Russian news agencies quoted Basurin as saying.

Basurin also rejected the idea that civilians may still be trapped in the industrial zone.

"There are no civilians there now," he was quoted as saying.