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.
The Azov regiment released drone footage showing explosions at the steelworks, but the date of the footage could not be verified. Earlier on Thursday Sviatoslav Palamar, an Azov regiment commander, said Ukrainian defenders were fighting "difficult, bloody battles" with Russian troops who had managed to enter part of the complex.
But the Kremlin denied its forces had tried to storm the plant and insisted that a humanitarian corridor was open as part of a three-day ceasefire that started on Thursday.
Mr Guterres said a third operation to evacuate civilians from the city was under way and would arrive in the city on Friday. Ukrainian Deputy Prime Minister Iryna Vereshchuk said on social media that this would happen at about midday.
At least 20 children are thought to be among the remaining civilians in the steelworks, and food and water supplies are dwindling fast.
On Sunday an initial group of civilians was evacuated from the plant. Footage showed mainly women and children being helped to walk over piles of rubble, and boarding a bus with missing windows.
Russia launched its invasion of Ukraine 10 weeks ago but has not yet gained full control over any of Ukraine's major cities.
In other developments:
- The US provided intelligence that helped Ukraine sink the Russian warship Moskva, multiple US media outlets report. Officials said Ukraine had asked the US about a ship in the Black Sea. The US identified it as the Moskva and helped confirm its location. Ukraine then targeted the ship
- Israel says Mr Putin has apologised after his foreign minister said that Nazi leader Adolf Hitler had "Jewish blood". Russia's account of the conversation did not mention an apology. Sergei Lavrov made the initial comments to try to justify Russia's portrayal of Ukraine as "Nazi" despite the fact that its president is Jewish
- A key ally of Russia, authoritarian Belarusian leader Alexander Lukashenko, has indicated that the war in Ukraine has not gone to plan. He told the AP news agency that the operation had "dragged on"
- The EU is close to agreeing on a sixth round of sanctions against Russia, the bloc's foreign policy chief says. On Wednesday the EU Commission proposed phasing out Russian oil imports entirely
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