Ukraine’s president Volodymyr Zelenskiy has called for more weapons, describing “every delay” as “permission for Russia to take the lives of Ukrainians”. In his latest address, he appealed to countries to send arms, saying Ukraine’s fate “depends upon them”.

Zelenskiy also claimed in the address that the regions of Kherson and Zaporizhzhia in Ukraine’s south were being transferred to “the ruble zone” and subordinated to Russian administration. The Ukrainian president said Russia’s actions in the territories were following the example of the so-called separatist republics of the DPR and LPR.

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.

A second British soldier fighting with the Ukrainian army was paraded on Russian television after being captured in Mariupol. Shaun Pinner, 48, said he had been fighting alongside Ukrainian marines when Vladimir Putin’s forces invaded nearly eight weeks ago.

Ukraine has completed a questionnaire which will form a starting point for the European Union to decide on membership for Kyiv, Ihor Zhovkva, deputy head of President Volodymyr Zelenskiy’s office, said.

A fresh series of Russian airstrikes came as a reminder this weekend that the war in the Ukrainian capital is far from over, despite signs of more normal life returning to the streets in recent days.

An unverified photo claiming to show the Russian warship Moskva moments after it was reportedly hit by a Ukrainian Neptune missile has surfaced online. The source of the image is unclear and the Guardian has not been able to immediately verify its authenticity.

Zelenskiy said he has invited French President Emmanuel Macron to visit Ukraine to see for himself evidence that Russian forces have committed “genocide”, a term Macron has avoided using.

Earlier on Sunday Zelenskiy urged US president Joe Biden to visit Ukraine and reiterated that he is not willing to cede territory in the country’s east to end war with Russia. Zelenskiy said he was “hopeful” Biden would make the trip.

The president of the European Commission has urged member states to supply Ukraine with weapons systems “quickly” and suggested that a next round of EU sanctions could target Russia’s powerful Sberbank.

The International Monetary Fund’s managing director, Kristalina Georgieva, said she had a “very good call” with Ukraine’s president. She added: “Continued economic support by Ukraine’s partners is essential to lay the foundations for rebuilding a modern competitive Ukraine.”

The United Nations refugee agency said 4,869,019 Ukrainians had left the country since Russia invaded in February – up 32,574 from Saturday’s total, the UN High Commissioner for Refugees chief, Filippo Grandi’s, said on Sunday.

Oleg Synegubov, head of the Kharkiv regional administration, said Ukrainian forces were successfully pushing the Russians back to the east of the city and that several villages were liberated.

At least two people were killed and four injured on Sunday in the shelling of the eastern Ukrainian town of Zolote, the local governor said.