Russian missile strikes have hit Ukraine's capital Kyiv and other cities, as Moscow says its troops had cleared the urban area of Mariupol and only a small contingent of Ukrainian fighters remain inside a steelworks in the besieged southern port.
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Russia's claim to have all but taken control of Mariupol, scene of the war's heaviest fighting and worst humanitarian catastrophe, could not be independently verified. It would be the first major city to have fallen to Russian forces since the February 24 invasion.
"The situation is very difficult" in Mariupol, President Volodymyr Zelenskiy told the Ukrainska Pravda news portal.
"Our soldiers are blocked, the wounded are blocked. There is a humanitarian crisis ... Nevertheless, the guys are defending themselves."
Russia's defence ministry said if Ukrainian forces in the giant Azovstal steelworks lay down their arms starting at 0300 GMT on Sunday (1300 AEST), their lives would be spared, Tass news agency said. There was no immediate response from Kyiv.
As Moscow launched long-range missile attacks across the country following the sinking of its Black Sea flagship, Moscow said its warplanes had struck a tank repair factory in Kyiv on Saturday.
The Ukrainian military said Russian warplanes that took off from Belarus had fired missiles at the Lviv region near the Polish border and four cruise missiles were shot down by Ukrainian air defences.
The western city has been relatively unscathed so far and serves as a haven for refugees and international aid agencies.
In Mariupol, Reuters journalists in Russian-held districts reached the Ilyich steelworks, one of two metals plants where defenders had held out in underground tunnels and bunkers. Moscow claimed to have captured it on Friday.
The factory was reduced to a ruin of twisted steel and blasted concrete, with no sign of defenders present. Several bodies of civilians lay scattered on nearby streets.
The Russian defence ministry said its troops had "completely cleared" Mariupol's urban area of Ukrainian forces and blockaded the "remnants" in the Azovstal steelworks, RIA news agency said.
Later on Saturday, Zelenskiy accused Russia of "deliberately trying to destroy everyone" in Mariupol and said his government was in touch with the defenders.
In Mykolaiv, a city close to the southern front, Russia said it had struck a military vehicle repair factory.
The attacks followed Russia's announcement on Friday it would intensify long-range strikes in retaliation for unspecified acts of "sabotage" and "terrorism", hours after it confirmed the sinking of its Black Sea flagship, the Moskva.
Kyiv and Washington say the ship, whose sinking has become a symbol of Ukrainian defiance, was hit by Ukrainian missiles. Moscow says it sank after a fire and its crew of around 500 were evacuated.
A month and a half into President Vladimir Putin's invasion of Ukraine, Russia is trying to capture territory in the south and east after withdrawing from the north following an assault on Kyiv that was repelled at the capital's outskirts.
Russian troops that pulled out of the north left behind towns littered with bodies of civilians, evidence of what US President Joe Biden this week called genocide.
Russia denies targeting civilians and says the aim of its "special military operation" is to disarm its neighbour, defeat nationalists and protect separatists in the southeast.
If Mariupol falls it would be Russia's biggest prize of the war so far. It is the main port of the Donbas, a region of two provinces in the southeast which Moscow demands be fully ceded to separatists.
Ukraine says it has so far held off Russian advances elsewhere in the Donbas regions of Donetsk and Luhansk, where at least one person was killed in shelling overnight.
Ukraine gained the upper hand in the early phase of a war, in part by successfully deploying mobile units armed with anti-tank missiles supplied by the West against Russian armoured convoys confined to roads by muddy terrain.
But Putin appears determined to capture more Donbas territory to claim victory in a war that has left Russia subject to increasingly punitive Western sanctions and with few allies.
Zelenskiy said about 2500-3000 Ukrainian troops have been killed so far and up to 20,000 Russian troops.
Moscow has given no updates on its casualties since March 25, when it said 1351 had died. Western estimates of Russian losses are many times higher.
Ukraine says civilian deaths are impossible to count, estimating at least 20,000 killed in Mariupol alone.
Overall, around a quarter of Ukrainians have been driven from their homes, including a tenth of the population that has fled abroad.
Australian Associated Press
