Ukrainian soldiers resisted a Russian ultimatum to lay down arms on Sunday in the pulverised port of Mariupol, which Moscow said its forces had almost completely seized in what would be its biggest prize of the nearly two-month war.

Ukrainian Prime Minister Denys Shmyhal said troops in Mariupol were still fighting despite a Russian demand to surrender by dawn.

“The city still has not fallen,” he told ABC’s “This Week” programme, adding that Ukrainian soldiers continue to control some parts of the city.

Russia said on Saturday it had control of urban parts of the city, with some Ukrainian fighters remaining in the Azovstal steelworks overlooking the Sea of Azov. Capturing Mariupol, the main port in the southeastern region of Donbas, would be a strategic prize for Russia, connecting territory held by pro-Russian separatists in the east with the Crimea region that Moscow annexed in 2014.

After failing to overcome Ukrainian resistance in the north, the Russian military has refocused its ground offensive on Donbas while maintaining long-distance strikes elsewhere, including capital Kyiv.

About four million Ukrainians have fled the country, cities have been shattered and thousands have died since the start of the invasion on February 24. “The occupiers will be responsible for everything they did in Ukraine,” President Volodymyr Zelensky said on his Telegram account, posting images of destruction he said were akin to the “terrible times” of World War II.

Zelensky accused Russia on Saturday of “deliberately trying to destroy everyone” in Mariupol and said his government was in touch with the defenders.

The Azovstal steelworks, one of Europe’s biggest metallurgical plants with a maze of rail tracks and blast furnaces, has become a last stand for the outnumbered defenders.

“All who lay down their arms are guaranteed that their lives will be spared,” Russia’s defence ministry said.

It was not known how many soldiers were in the steelworks. Satellite images have shown smoke and fire coming from the area, which is riddled with tunnels. Zelensky has said killing his troops would put paid to peace efforts.

Russia said Ukraine had lost more than 4,000 soldiers in Mariupol as of Saturday. Kyiv says its total troop losses nationwide so far in the war are less than that, between 2,500 and 3,000. Reuters has not been able to verify either side’s figures.

Ukrainian foreign minister Dmytro Kuleba said in a CBS News interview on Sunday there had not been any recent communications between Russia and Ukraine at a foreign-ministry level, and that the situation in Mariupol, which he described as “dire”, could be a “red line” in the path of negotiations.

Elsewhere in Ukraine, there were more reports on Sunday of Russian strikes around major population centres.

Local media reported an explosion in Kyiv, though deputy mayor Mykola Povoroznyk said air defence systems had thwarted Russian attacks. The mayor of Brovary city, close to Kyiv, said a missile attack had damaged infrastructure.

Russia said it had destroyed an ammunition factory near the capital, according to the RIA news agency.

Shelling in Ukraine’s second biggest city, Kharkiv, killed five people and injured 13, Ukrainian public broadcaster Suspilne reported. A Reuters correspondent in Kharkiv heard multiple explosions in quick succession and saw debris from missiles.

As clean-up operations continued in areas where the Russians have retreated, Ukraine’s human rights ombudswoman said almost all high-rise buildings in the town of Okhtyrka were unfit for occupation. The State Emergencies Service said 41 bodies had been recovered in the town of Borodyanka.

Most Ukrainians celebrate Orthodox Easter next Sunday, but in Bucha, a town north of Kyiv where Ukraine accuses Russia of killing dozens of civilians, some 50 people attended a church service, carrying pussy willow and praying for the dead.

Russia denies targeting civilians and has called images from Bucha fake.

“I just prayed today to stop crying,” said resident Evgeniya Lebedko after the service.