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 three hours after the ultimatum took effect at 0300 GMT in the strategic southeastern port.
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 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 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 that the defenders could leave the plant by 10:00 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 km, containing myriad buildings, blast furnaces and rail tracks.
The city's defenders include Ukrainian marines, motorised brigades, a National Guard brigade and the Azov Regiment, a militia created by far-right nationalists that was later incorporated into the National Guard. It was not immediately known how many were in the steelworks.
"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.