There was no immediate confirmation from Ukraine.
A three-month siege has reduced much Mariupol to a smoking ruin, with over 20,000 civilians feared dead
Russian Defence Minister Sergei Shoigu reported to President Vladimir Putin the "complete liberation" of the steelworks — the last stronghold of Ukrainian resistance — and the city as a whole, spokesman Igor Konashenkov said.
Russia's state news agency RIA Novosti quoted the ministry as saying a total of 2,439 Ukrainian fighters who had been holed up at the steelworks had surrendered since Monday, including over 500 on Friday.
A Russian state TV correspondent said on Telegram that among those surrendering was Denys Prokopenko, commander of the Azov regiment.
Prokopenko said on Friday that the defenders of Mariupol — a group of Ukrainian fighters from various military and law enforcement units —- had received an order to "cease the defence of the city."
The intention is to "save lives and health of the servicemen of the garrison," he said.
Speaking in a video statement where he appeared with his arm bandage, Prokopenko also said that "the seriously wounded received the necessary assistance and they were able to be evacuated with further exchange and delivery to the territory controlled by Ukraine."
Ukraine President Volodymyr Zelenskyy says Russia must be held financially responsible for the damage its forces are inflicting on his country.
In his latest nightly address, Zelenskyy said Russia should be made to pay for every home, school, hospital and business it destroys.
He said a legal mechanism should be created through which everyone who suffered from Russia's actions would be able to receive compensation.
Zelensky said Ukraine wanted its partners to seize Russian funds and property under their jurisdiction and use them to create a fund for those who suffered from Russian aggression.
He noted, that on Friday the Russian army fired a missile at the northeastern Kharkiv region, destroying a cultural centre in Lozova, and also hit the cities of Odesa in the south, Poltava in the east and Zhytomyr in the west.
Zelenskyy's social media channel released video showing a large explosion hitting the newly renovated Palace of Culture in Lozova. Seven people were injured, including a child.
"The occupiers identified culture, education and humanity as their enemies," Zelenskyy wrote. "What is in the minds of people who choose such targets? Absolute evil, absolute stupidity."
In the eastern Donbas, where the Russian attack has been fiercest, he said Russian troops turned the towns of Rubizhne and Volnovakha into ruins, just as they did with Mariupol, and were trying to do the same with Severodonetsk.
The President also revealed in an interview that Ukrainian pilots had risked Russian anti-aircraft fire to fly medicine, food and water supplies to the Mariupol steel mill on helicopters, suffering a large amount of casualties.
To save what he called the "heroes" holed up in the ruined remains of the steel mill, "a very large number of people, our pilots, were killed" in the operation.
"They are absolutely heroic people, who knew that it would be difficult, knew that to fly would be almost impossible," Zelenskyy said.
He said the airlift couldn't be reported earlier because no safe air corridor to the plant had been established, and that powerful anti-aircraft weapons were in place.
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