KYIV, Ukraine (AP) — The shattered port city of Mariupol appeared on the brink of falling to the Russians on Sunday 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 estimated 2,500 Ukrainian fighters were 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.”

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 where the Kremlin has focused its war aims after failing in its bid to take take Kyiv, Ukraine’s capital.

The relentless bombardment and street fighting in Mariupol have killed at least 21,000 people, by the Ukrainians’ estimate. A maternity hospital was hit by a lethal Russian airstrike in the opening weeks of the war, and about 300 people were reported killed in the bombing of a theater where civilians were taking shelter.

An estimated 100,000 remained in the city out of a prewar population of 450,000, 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,” Maj. Gen. Igor Konashenkov, the Russian Defense Ministry’s spokesman, said in announcing the latest ultimatum.

He said intercepted communications indicated there were about 400 foreign mercenaries holed up along with the Ukrainian troops at the Azovstal steel mill, which covers more than 11 square kilometers (4 square miles) and is laced with tunnels.

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 Ukraine is safe, Russian forces carried out missile strikes Sunday near Kyiv and elsewhere in an apparent effort to weaken Ukraine’s military capacity before the anticipated assault.

After the humiliating sinking of the flagship of Russia’s Black Sea Fleet last week in what the Ukrainians boasted was a missile attack, the Kremlin had vowed to step up strikes on the capital.

The Kremlin said Sunday that it had attacked an ammunition plant near Kyiv overnight with precision-guided missiles, the third such strike in as many days.

Explosions were reported overnight in Kramatorsk, the eastern city where rockets earlier this month killed at least 57 people at a train station crowded with civilians trying to evacuate ahead of the Russian offensive.

A regional official in eastern Ukraine said at least two people were killed when Russian forces fired at residential buildings in the town of Zolote, near the front line in the Donbas.

At least five people were killed by Russian shelling in Kharkiv, Ukraine’s second-largest city, on Sunday, regional officials said. The barrage slammed into apartment buildings and left the streets scattered with broken glass and other debris, including part of at least one rocket.

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.

Malyar, the Ukrainian deputy defense minister, said the Russians continued to hit Mariupol with airstrikes and could be getting ready for an amphibious landing to reinforce their ground troops.

Capturing the southern city of the Sea of Azov would allow Russia to fully secure a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014, and deprive Ukraine of a major port and its prized industrial assets.

The looming offensive in the east, if successful, would give Russian President Vladimir Putin a vital piece of the country and a badly needed victory that he could sell to the Russian people amid the war’s mounting casualties and the economic hardship caused by the West’s sanctions.

Austrian Chancellor Karl Nehammer, who met with Putin in Moscow this week — the first European leader to do so since the invasion Feb. 24 — said the Russian president is “in his own war logic” on Ukraine.

In an interview on NBC’s “Meet the Press,” Nehammer said he thinks Putin believes he is winning the war, and “we have to look in his eyes and we have to confront him with that, what we see in Ukraine.’’

Without explicitly mentioning Putin’s decision to invade, Pope Francis made an anguished Easter Sunday plea for peace in Ukraine, decrying “this cruel and senseless war into which it was dragged.”

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Chernov reported from Kharkiv. Yesica Fisch in Kramatorsk, Ukraine, and Associated Press journalists around the world contributed to this report.