The shattered port city of Mariupol appears on the brink of falling to the Russians in what would give Moscow its biggest victory of the war yet and free up troops to take part in a potentially climactic battle for control of Ukraine’s industrial east.

Russia estimates 2500 Ukrainian fighters are holding out at a hulking steel plant in the last pocket of resistance in Mariupol, much of which has been reduced to a smoking ruin during a merciless seven-week siege.

Moscow gave the city’s defenders a surrender-or-die ultimatum with a midday deadline, saying those who laid down their arms were “guaranteed to keep their lives.” But the fighters ignored it, just as they rejected previous ultimatums.

“We will fight absolutely to the end, to the win, in this war,” Ukrainian Prime Minister Denys Shmyhal vowed on ABC’s “This Week.”

He said Ukraine is prepared to end the war through diplomacy if possible, “but we do not have intention to surrender”.

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Ukrainian President Volodymyr Zelenskyy sent Easter greetings via Twitter, saying: “The Lord’s Resurrection is a testimony to the victory of life over death, good over evil.”

If Mariupol is captured, Russian forces there are expected to join an all-out offensive in the coming days for control of the Donbas, the eastern industrial region that the Kremlin is bent on taking after failing in its bid to seize Kyiv, Ukraine’s capital.

The relentless bombardment and street fighting in Mariupol have killed at least 21,000 people, by the Ukrainians’ estimate.

An estimated 100,000 remained in the city out of a prewar population of 450,000. They are trapped without food, water, heat or electricity in a siege that has made Mariupol the scene of some of the worst suffering of the war.

“All those who will continue resistance will be destroyed,” Major General Igor Konashenkov, the Russian Defense Ministry’s spokesman, said in announcing the latest ultimatum.

He said intercepted communications indicated about 400 foreign mercenaries were holed up along with the Ukrainian troops at the Azovstal steel mill, which covers more than 11 square kilometres and is laced with tunnels.

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Ukrainian Deputy Defense Minister Hanna Malyar described Mariupol as a “shield defending Ukraine” as Russian troops prepare for the battle in the mostly Russian-speaking Donbas, where Moscow-backed separatists already control some territory.

In a reminder that no part of the country is safe, Russian forces carried out missile strikes on Sunday near Kyiv and elsewhere in an apparent effort to weaken Ukraine’s military capacity before the anticipated assault.

Explosions were reported overnight in Kramatorsk; a regional official in eastern Ukraine said at least two people were killed when residential buildings were hit in the town of Zolote; and at least five people were killed by Russian shelling in Kharkiv, Ukraine’s second-largest city.

Russia also said that its forces shot down two Ukrainian MiG-29 fighter jets in the Kharkiv region and destroyed two Ukrainian command posts and a radar system for S-300 surface-to-air missiles in the city of Avdiivka, north of Donetsk city.

Ukrainian officials did not immediately confirm the claimed losses.

-AAP