In a mission carried out with the support of the United Nations, civilians were rescued from tunnels as Ukrainian soldiers continued to defend the plant in a bid to prevent Moscow's complete takeover of the strategic port city.
There are thought to be about 200 civilians, including at least 20 children, trapped with up to 2,000 Ukrainian fighters under the Mariupol plant. The Ukrainian authorities have said almost 500 civilians have been safely evacuated from the city since the UN-led rescue operation began.
A bus carrying a further 12 people, some of them believed to be children, left the plant on Friday afternoon.
However, there has been growing speculation Russian president Vladimir Putin wants to finish the battle for Mariupol so he can present a triumph to the Russian people in time for Monday's Victory Day – the biggest patriotic holiday on the Russian calendar. Mr Putin said that Ukraine should order its fighters to surrender the city.
This comes as Ukrainian president Volodymyr Zelensky challenged German Chancellor Olaf Scholz to meet him for talks in Kyiv, suggesting the visit could also take place on on May 9.
Speaking at an event held by the Chatham House think-tank, the Ukrainian president said the move would be a "very powerful political step".
Asked whether Ukraine was satisfied with the support it was getting, particularly from EU nations including Germany, and what he would say to Mr Scholz if he had the chance to speak with him, Mr Zelensky said: "You cannot be slightly evil and slightly good.
"With the right hand you impose sanctions, with the left hand you sign the Russian contracts. This is not right. This is hypocrisy."
He added: "I think Chancellor Scholz, for him ... he's invited – the invitation is open, it's been for some time now. He's invited to come to Ukraine. He can make this very powerful political step to come here on May 9, to Kyiv.
"Sometimes in history we have to make certain steps for unity, even if there is some kind of coldness in specific relations."
Ukraine said a total of 500 people had been rescued from Mariupol during the evacuation.
"We conducted another stage of a complex operation to evacuate people from Mariupol and Azovstal,” the head of Ukraine's presidential office, Andriy Yermak, said. “I can say that we managed to take out almost 500 civilians."
It was not clear if that figure referred entirely to new evacuations or included around 100 people who were rescued over the weekend in a United Nations-assisted operation.
It was also not clear how many might be left underground, but UN secretary-general Antonio Guterres said on Thursday the organisation "must continue to do all we can to get people out of these hellscapes".
People escaping Mariupol typically have to pass through contested areas and many checkpoints – sometimes taking days to reach relative safety in the Ukrainian-controlled city of Zaporizhzhia, about 140 miles to the north west.
Ahead of Victory Day, which marks the Soviet Union's triumph over Nazi Germany, municipal workers and volunteers cleaned up what remains of Mariupol, a city that is now under Russia's control apart from the steel plant.
Bulldozers scooped up debris and and people swept streets, with a backdrop of buildings hollowed out by shelling. Workers repaired a model of a warship and Russian flags were hoisted on utility poles.
The fall of Mariupol would deprive Ukraine of a vital port, allow Russia to establish a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014, and free up troops to fight elsewhere in the Donbas, the eastern industrial region the Kremlin says is now its chief objective.
Its capture also holds symbolic value since the city has been the scene of some of the worst suffering of the war and a surprisingly fierce resistance.
While they pounded away at the plant, Russian forces struggled to make significant gains elsewhere, ten weeks into a devastating war that has killed thousands of people, forced millions to flee the country and flattened large swathes of cities.
The Ukrainian military's General Staff said on Friday its forces repelled 11 attacks in the Donbas and destroyed tanks and armoured vehicles, further frustrating Mr Putin's ambitions after his abortive attempt to seize Kyiv.
Russia gave no immediate acknowledgement of those losses.
Ukrainian chief of defence, General Valerii Zaluzhnyi, meanwhile said on Thursday that a counter-offensive could begin to push Russian forces away from Kharkiv and Izyum – two cities key to the Russian campaign in the Donbas, where Moscow-backed separatists have been fighting Ukrainian troops for eight years.
Already, Ukrainian fighters have driven Russian troops some 25 miles east of Kharkiv in recent days.
The extended stand-off at the plant in Mariupol was helping to hinder Russia's plans for the Donbas, the British Ministry of Defence said in an assessment on Friday.
The fighting at the plant "has come at personnel, equipment and munitions cost to Russia", it said. "Whilst Ukrainian resistance continues in Azovstal, Russian losses will continue to build and frustrate their operational plans in southern Donbas."
The Ukrainians say Russian troops have stormed the steelworks and are also striking it from the air, but the wife of one commander at the plant said they had vowed to "stand till the end".
"They won't surrender," Kateryna Prokopenko said after speaking by phone to her husband Denys Prokopenko. "They only hope for a miracle."
The Russians have pulverised much of Mariupol, which had a pre-war population of more than 400,000, and a two-month siege that has trapped perhaps 100,000 civilians with little food, water, electricity or heat.
Civilians sheltering inside the plant have perhaps suffered even more, hunkering underground without seeing daylight in months.