A third operation to pull civilians from Mariupol is due on Friday, the UN says, as more fighting was reported for control of a steelworks where the last Ukrainian defenders are holding out.
About 200 civilians are also believed to be hiding in bunkers in the plant.
UN chief Antonio Guterres said everything should be done to “get people out of these hellscapes”.
Russia’s Vladimir Putin said his forces are ready to give civilians safe passage, but fighters must surrender.
The Russian president has already declared victory in Mariupol, ordering his forces to seal off the sprawling industrial site – which was designed during the Cold War to serve as a nuclear bunker and has a network of tunnels deep below ground – rather than try to take control of it.
However the remaining Ukrainian forces inside the steelworks – fighters from the Azov regiment, some marines, border guards and police – say Russian attacks are continuing.
In his overnight address Ukraine’s President Zelensky also said that Russian shelling and attempts to wrest control of the steelworks were ongoing.
“Just imagine this hell. And there are children! More than two months of constant shelling, bombing, constant death nearby,” he said.