Ukraine has refused to surrender Mariupol, rejecting a demand from Russia to give up the city by the deadline of 05:00 Moscow time (02:00 GMT).
Russia had offered to set up humanitarian corridors so residents could leave in exchange for the city.
About 300,000 people remain trapped with little if any food, water and power in the city which has been incessantly bombed for the past two weeks.
Russia has struck several civilian shelters, schools, a hospital and a theatre.
Ukraine has said the Mariupol attacks are war crimes that will go down in history.