Kyiv, Ukraine - The Ukrainian military continued to brace itself on Sunday for a major new offensive by Russian troops in eastern Ukraine as the dust settled on the sinking of Russia's Black Sea Fleet flagship, the Moskva, late on Thursday.

Moscow and Kyiv continued to issue statements that were starkly at odds with each other, with Moscow claiming on Saturday that over 23,000 Ukrainian soldiers and foreign fighters had lost their lives since the start of the war.

Ukrainian President Volodymyr Zelensky, on the other hand, put the number of Ukrainian deaths in the conflict to date at between 2,500 and 3,000 in an interview published on Friday.

Russian Defence Ministry spokesperson Igor Konashenkov said on Saturday that over 4,000 Ukrainians had been killed in the battle for Mariupol alone, and that all remaining Ukrainian fighters in the fiercely contested Azov Sea port were now encircled inside the city's Azovstal steelworks.

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Zelensky threatened to withdraw from the ongoing peace negotiations with Russia if the remaining Ukrainian fighters trapped in Mariupol were killed by the Russian forces besieging the city.

"What they are doing right now... could put a stop to any form of negotiation," Zelensky said in an interview with a Ukrainian news website published on Saturday.

"There are troops there who absolutely hate them, and I don't think they will let them live," the Ukrainian leader said, referring to the fact that many of the fighters trapped in the city are part of the Azov Battalion, whose far-right leanings have been the subject of Russian media reports for weeks.

Later on Saturday in a video address, Zelensky called the situation in Mariupol "just inhuman."

"This is what the Russian Federation did. Deliberately did. And deliberately continues to destroy cities. Russia is deliberately trying to destroy everyone who is there in Mariupol," the Ukrainian leader said, calling on international partners to arm his country "immediately" so Kyiv can "reduce the pressure of the occupiers on Mariupol and unblock it."

Meanwhile, the Russian army again called on Ukrainian forces in Mariupol to surrender.

Taking into account the "catastrophic" in the Azovstal steelworks, the trapped Ukrainian fighters and "foreign mercenaries" are being offered to cease hostilities and lay down their arms from 6:00 AM local time on Sunday, said a statement of Major General Mikhail Mizintsev of the Russian Defence Ministry early on Sunday.

"All those who lay down their arms are guaranteed life," Mizintsev said.

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Elsewhere, several people were killed in renewed Russian attacks on the Ukrainian capital Kyiv and second city Kharkiv on Saturday, as tens of thousands of Russian troops were reported to be regrouping in eastern Ukraine ahead of the expected fresh assault on the Donbass, according to the governor of the Luhansk region, Serhiy Hayday.

Hayday also noted the transfer of large amounts of military equipment and technology to the region. "They already have everything ready for a breakthrough," Hayday said, adding that the Russian troops were only waiting for better weather before launching simultaneous attacks on the Luhansk and Donetsk regions.

Rain in both regions was due to stop by the middle of next week, according to weather forecasts.

In the Ukrainian capital there were several explosions in the south-eastern district of Darnytsia on Saturday, according to a Telegram post by Kyiv Mayor Vitali Klitschko.

One person was killed in the attacks, according to the Ukrainian side. Several were taken to hospital with life-threatening injuries, Klitscko said on television.

The mayor appealed to the population not to ignore the multiple daily air raid sirens in the capital as more Russian airstrikes were reported.

The situation is especially dangerous at the moment as many of those who fled the capital at the start of the war are now returning in light of Russia's apparent military redeployment to the east.

Klitschko warned people against planning to return to Kyiv for the time being, urging them instead to remain in safer places elsewhere.

Moscow recently threatened to attack command centers in Kyiv after accusing the Ukrainian military of shelling Russian territory, and confirmed its renewed shelling of Kyiv, saying that it had targeted and destroyed production facilities at a tank factory.

Defense Ministry spokesman Igor Konashenkov said Russian forces had also destroyed a tank repair facility and two warehouses storing missiles and artillery in the southern city of Mykolaiv.

In Kharkiv, at least one person was reportedly killed and 18 injured in an attack on Saturday. Attacks were also reported in the Lviv region of western Ukraine and at a military airfield in Olexandriya in central Ukraine.

Ahead of the expected Russian offensive in the Donbass region, a senior advisor to Zelensky, Mykhailo Podolyak, expressed his frustration at the slow pace of promised arms deliveries from the European Union.

While the EU was supporting Ukraine with weapons, they were "not the ones we asked for," Podolyak tweeted on Saturday. Moreover, he said, the deliveries were taking too long. "Ukraine needs weapons. Not in a month. Now," he wrote.

Ukrainian Deputy Prime Minister Iryna Vereshchuk told national television on Saturday that the Russian military had taken more than 1,000 Ukrainians prisoner, including hundreds of civilians, of whom around 500 were women.

Ukraine, for its part, had captured about 700 Russian soldiers, Vereshchuk said. She called on Russia to release the civilians unconditionally. Since the start of the war, Moscow and Kyiv have done several prisoner exchanges.