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".
Local media reported an explosion in the capital Kyiv but Mykola Povoroznyk, the city's deputy mayor, said there were no explosions and air defence systems had prevented Russian attacks.
Russia's Defence Ministry said on Saturday its troops had cleared the urban area of Mariupol and only a small contingent of Ukrainian fighters remained in a steelworks.
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 February 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 06:00 (Moscow time) on April 17, 2022, to stop any hostilities and lay down their arms," the defence ministry said in a statement.
"All who lay down their arms are guaranteed that their lives will be spared," it said, adding the defenders could leave the plant by 10 am without arms or ammunition.
There was no immediate response from Kyiv.
The Azovstal plant, described as a fortress in a city, lies in an industrial area that looks out to the Sea of Azov and covers more than 11 square kilometres.
"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."
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, relatively unscathed so far, has served as a haven for refugees and international aid agencies.
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.
It said that as of Saturday, Ukrainian forces in the city had lost more than 4000 personnel.
Zelenskiy accused Russia of "deliberately trying to destroy everyone" in Mariupol and said his government was in touch with the defenders.
He did not address Moscow's claim Ukrainian forces were no longer in urban districts.
He added that "extermination" of the fighters in Mariupol would put an end to any form of negotiations with Russia.
Russia had said 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.
Russia's Defence Ministry published video of the head of the navy, Admiral Nikolai Yevmenov, meeting on a parade ground with about a hundred sailors it said were members of the crew.
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.
