Ukrainian officials say Russian forces have launched an all-out assault on the Azovstal steelworks, the last Ukrainian holdout in the city of Mariupol.
Ukrainian forces inside the plant have been fighting "difficult bloody battles" for a second day, the commander of the Azov regiment said.
Russian forces are reported to have entered "the territory of the plant" after days of sustained attacks.
About 200 civilians are believed to be sheltering inside, including children.
The BBC has not been able to verify the reports of the Russian attack on the steel plant.
In a brief video message posted on Telegram, Azov commander Denis Prokopenko said: "I am proud of my soldiers who are making superhuman efforts to contain the pressure of the enemy... the situation is extremely difficult."
President Volodymyr Zelensky has made a further appeal to the UN to help save the lives of those who remain there.
"Everyone is important to us. We ask for your help in saving them," Mr Zelensky told UN Secretary General Antonio Guterres in a phone call.
The Ukrainian leader thanked Mr Guterres for a successful UN and Red Cross-led evacuation this week, which rescued more than 100 people from the steelworks, but called on the UN to "assist in the removal of all the wounded from Azovstal".
There were also more evacuations from other areas - Ukraine's deputy prime minister said that 344 evacuees from various south-western cities including Mariupol arrived in the relative safety of Zaporizhzhia on Wednesday - a south-eastern city still under Ukrainian control.
In a post on Telegram, Irina Vereshchuk thanked the UN and Red Cross for their help, saying: "These are women, children and elderly people from Mariupol, Manhush, Berdiansk, Tokmak and Vasylivka... We will now support them during this difficult time, including with much-needed psychological support."
Osnat Lubrani, the UN's humanitarian coordinator for Ukraine, confirmed the evacuations.
"While this second evacuation of civilians from areas in Mariupol and beyond is significant, much more must be done to make sure all civilians caught up in fighting can leave, in the direction they wish," she said in a statement.
Today again, we managed to provide safe passage for civilians stranded in Mariupol & other areas, thanks to a strong @UN - @ICRC collaboration.— Osnat Lubrani (@OsnatLubrani) May 4, 2022
Many came with nothing but the clothes they had on. We will now support them in this difficult time.
Our work must, and will continue. pic.twitter.com/LiWvUiFaOf
Russian ceasefire promised
Russia has said it will implement a ceasefire from Thursday to allow more civilian evacuations from the Azovstal plant.
The Russian military said routes out of the plant would open from 08:00 to 18:00 Moscow time (05:00 to 15:00 GMT) on 5, 6, and 7 May.
During this time, Russian forces will cease activities and withdraw units to a safe distance, the military said in a post online.
Meanwhile, new analysis suggests many as 600 people were killed when Russia bombed a theatre in Mariupol in March. The attack is believed to have caused the worst known loss of life in a single strike since the invasion began.
An investigation by the Associated Press (AP) news agency now puts the death toll at about double the previous estimate of 300. AP spoke to 23 survivors, rescuers and those familiar with the theatre's use as a bomb shelter.
Russian troops have spent weeks besieging and bombarding Mariupol, which is key to Moscow's military campaign in Ukraine.
Full control of the city would give the Russians a land bridge from Russia, through parts of the Donbas region held by Russian-backed separatists, right through to Crimea, which Russia annexed in 2014.
Despite indications that Russia is making slow progress in its effort to invade and retain southern and eastern parts of the country, the Kremlin has dismissed speculation that it will declare all-out war in Ukraine in the coming days as "nonsense".
Moscow has up until now denied it is at war, instead referring to the invasion as a "special military operation".
But Western officials have speculated that President Vladimir Putin could use the 9 May Victory Parade to announce an escalation of military action. Moscow has denied this.