Russian forces edge closer to control of port city whose fall would deal economic blow to Kyiv and symbolic victory for Moscow

• Russia-Ukraine war: latest updates

Ukraine has vowed that its forces will “fight to the end” in the besieged port city of Mariupol, after a Russian ultimatum for the remaining Ukrainian troops there to surrender expired.

Moscow is edging closer to full control of the city in what would be its biggest prize since it invaded Ukraine in February. Relentless bombardment and street fighting have left much of the city pulverised, killing at least 21,000 people by Ukrainian estimates.

Mariupol forces defy Russian demand for surrender, as European Commission chief urges fast supply of arms to Ukraine

• Russia-Ukraine war: latest updates

The remaining Ukrainian forces in the southern port city of Mariupol were still fighting on Sunday and continued to defy a Russian demand that they surrender, according to the Ukrainian prime minister, Denys Shmyhal.

The president of the European Commission, Ursula von der Leyen, urged member states to supply Ukraine with weapons systems “quickly” and suggested that a new round of EU sanctions could target Russia’s powerful Sberbank and include an embargo on Russian oil.

A Ukrainian health official said at least five people were killed in the Russian shelling of Kharkiv on Sunday. Maksym Haustov, the head of the Kharkiv regional administration’s health department, said another 13 residents were wounded in the bombardment of Ukraine’s second largest city.

At least two people were killed and four injured on Sunday in shelling of the eastern Ukrainian town of Zolote, the local governor said. “In one of the high-rise buildings, two floors were destroyed … we have at least two dead citizens, four more wounded,” said Serhiy Gaidai, the governor of Luhansk.

Ukraine and Russia failed to agree on humanitarian convoys for the evacuation of civilians from war-affected areas, according to Ukraine’s deputy prime minister, Iryna Vereshchuk.

Another missile attack in the early hours of Sunday damaged infrastructure in Brovary, near Kyiv, said the city’s mayor, Igor Sapozhko, in an online post.

Russian armed forces destroyed an ammunition factory near Kyiv, the Russian defence ministry spokesperson Igor Konashenkov said.

Many of the nearly 5 million people who have fled Ukraine will not have homes to return to, the United Nations warned.

Ukraine has asked G7 nations for $50bn (£38bn) in financial support and is also considering issuing 0% coupon bonds to help it cover a war-linked budget deficit over the next six months, the president’s economic adviser Oleg Ustenko said.

Russia said it was “concerned” about increased activity of Nato forces in the Arctic and that it saw risks of “unintended incidents” occurring in the region, Reuters reported.

In his Easter Sunday address, Pope Francis urged leaders to hear the people’s plea for peace in Ukraine and implicitly criticised Russia for dragging the country into a “cruel and senseless” conflict.

Christ’s message that good will triumph over evil resonated even more this year amid the backdrop of the war in Ukraine, Boris Johnson said.

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A missile attack in early hours of Sunday damaged infrastructure in the city of Brovary, near Ukraine’s capital of Kyiv, Igor Sapozhko, mayor of Brovary said in an online post.

There were no details on the extent of the destruction and potential casualties.

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Stay or go?

The question was a difficult one for Ukrainian officials in occupied areas, when deciding whether to follow President Volodymyr Zelenskiy’s lead after he made the decision to remain in Kyiv as Russia invaded.

During occupation the main thing is to preserve life, and the people most in danger are the heads of the city. If the city is occupied, what should the mayor do, what should the team do? There was no single algorithm. Nobody gave us any orders. Everyone acted as they felt right.”

The situation in Mariupol is difficult and hard. Fighting is happening right now. The Russian army is constantly calling on additional units to storm the city.”