Explosions were heard in the early hours on Sunday in Ukraine's capital, Kyiv, local media reported.
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Overnight, air raid sirens were going off over nearly all of Ukraine.
Meanwhile, Russia told Ukrainian forces fighting in Mariupol to lay down arms on Sunday morning to save their lives, but there were no immediate reports of activity two hours after the ultimatum took effect at 3:00 a.m. GMT.
Air raid sirens sounded across the country early in the day, a regular occurrence, and a morning report from the Ukrainian military said Russian air strikes on Mariupol continued while there were "assault operations near the seaport."
Russia's Defense Ministry said its troops had cleared the urban area of Mariupol and only a small contingent of Ukrainian fighters remained in a giant steelworks on Saturday.
Moscow'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 Feb. 24 invasion.
"Taking into account the catastrophic situation that has developed at the Azovstal metallurgical plant, as well as being guided by purely humane principles, the Russian Armed Forces offer the militants of nationalist battalions and foreign mercenaries from 6:00 (Moscow time) on April 17, 2022, to stop any hostilities and lay down their arms," the defense ministry said in a statement.
"All who lay down their arms are guaranteed that their lives will be spared," it said, adding that the defenders could leave the plant by 10 a.m. Sunday without arms or ammunition.
There was no immediate response from Kyiv.
A total of 1,449 people were evacuated from Ukrainian cities through humanitarian corridors on Saturday, fewer than the 2,864 who escaped on Friday, a senior official said.
Kyrylo Tymoshenko, deputy head of Ukraine's presidential administration, made the announcement in an online post.
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