IMAGE SOURCE,ED JONES/AFP/GETTY IMAGES
The Azovstal plant, which has become the last stronghold of Ukrainian resistance in the city, has been under intense Russian bombardment for weeks.
A commander at the plant, Denys Shlega, said while some civilians had been evacuated hundreds still remained.
He also said Russian forces had resumed heavy shelling of the area.
As soon as the civilians who had been evacuated left, "shelling from all kinds of weapons began", he told Ukrainian television.
He added that "several dozen small children are still in the bunkers underneath the plant".
A first group of evacuees from the steelworks are expected to arrive in the Ukrainian-controlled city of Zaporizhzhia later on Monday.
They were evacuated with the support of the UN and the International Committee of the Red Cross who organised an official convoy.
Russia said some evacuees had been taken to a village controlled by Moscow-backed separatists. But state media later reported that they would be free to travel onwards to Ukrainian-held territory if they wanted to.
Ukraine's President Volodymyr Zelensky welcomed the news that around 100 people were heading for Zaporizhzhia, which is about 140 miles (230km) north-west of Mariupol.
"Grateful to our team! Now they, together with UN, are working on the evacuation of other civilians from the plant," he wrote on Twitter.
Some people have spent many weeks sheltering in the Azovstal steelworks, with reports suggesting food, water and medicine supplies are all running low.
"The situation has become a sign of a real humanitarian catastrophe," the country's Deputy Prime Minister Iryna Vereshchuk said.
One Russian news report estimated the number of civilians still in the plant was more than 500.
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A few evacuees from Mariupol who had not been sheltering in the steelworks arrived in Zaporizhzhia earlier on Monday after travelling independently.
"We lived in [our] basement starting from 27 February," Natalya Tsyntomirska told Reuters news agency. "The whole time, we were shelled with mines, and then air strikes started. Our house is completely destroyed."
Another evacuee, who did not give a name, said she had been unable to reach the evacuation buses because of a blockade.
"Our city is divided between the left bank and right bank. The left bank was under a total blockade. We couldn't reach these buses," she said.
'It's been difficult, tough, frightening'
By Laura Bicker in Zaporizhzhia
A few civilians with their own cars are making use of the humanitarian corridor brokered by the United Nations and the Red Cross to get to the refugee centre.
Most of the vehicles are battered, one even had its windscreen smashed. Others are using plastic film and sticky tape to hold parts of the car together.
Daniil had to scramble through the city looking for spare parts for his car after it was hit by shrapnel from a shell which landed just five metres away. Peeking out the plastic film window from the passenger seat was his husky dog, Sly.
After handing over his papers to officials, Daniil jumped out the car and threw his hands in the air. His fingers made the V for victory sign.
"It's been difficult, tough, frightening. I lived on a tugboat in the port in Mariupol. We couldn't even raise our heads. It was so scary to be there," he said.
"Mariupol used to have a wonderful park. It was a prospering city. Now it's all gone."
I asked him what he will do now.
"I am going to leave. I am going to get as far from everything as possible."
Mariupol is almost fully under Russian control, but Ukrainian soldiers have continued to defend the steelworks.
Much of the city has been destroyed in weeks of heavy Russian bombardment and intense street fighting. Taking the port city is a key Russian war aim and would release more troops to join its offensive in the eastern Donbas region.
