The operation began a week ago, co-ordinated by the UN and Red Cross, which have not confirmed the news.
Ukrainian forces are holding out at the heavily bombed plant, the last part of the city not under Russian control.
Russia has besieged the plant for weeks, demanding the surrender of its defenders from the Azov battalion.
The whereabouts of the evacuees are not yet clear, but Ukrainian Deputy Prime Minister Iryna Vereshchuk said this part of the humanitarian operation was now complete. In the past, it has taken days for those evacuated to reach Ukrainian-held territory.
Ukrainian President Volodymyr Zelensky said more than 300 civilians had been rescued from the plant, although the Russian defence ministry gave a much lower number, saying 51 people had been evacuated over a period of three days.
Capturing Mariupol is important to Russian troops because it will allow them to complete a land bridge between Crimea and the Donbas region, as well as giving them full control of more than 80% of Ukraine’s Black Sea coastline.
But in their quest to do so, they have pummelled Mariupol with artillery, rockets and missiles – damaging or destroying more than 90% of the city.
Ukrainian fighters inside the Azovstal complex issued a statement on social media saying both they and the Russians had been using a white flag system to halt fighting to get civilian people out.
It sounds like progress between the two sides, and lives have been saved by these negotiations.
But Kremlin-backed forces have reportedly intensified their fire on the steel works in recent days, despite pledges of a ceasefire.
The previous UN and Red Cross operation to free more than 100 people was held up by land mines and mortar fire.
Now that the civilians are free, it puts new pressure on the Ukrainian government to find a way out for about 2,000 fighters using the site to make a last stand for the city of Mariupol – and who have vowed never to surrender.
Their families have issued a desperate plea to world leaders to negotiate their safe release.
Meanwhile, Russia has said there will be no Victory Day celebrations in Mariupol.
Victory Day is celebrated annually on 9 May in Russia to mark the Soviet Union’s victory in World War Two.
“A time will come and there will be a big celebration there,” Kremlin spokesman Dmitry Peskov told reporters, adding there were no plans for official visits on the day.
Ukraine’s armed forces said on Saturday that they had taken five villages north-east of the country’s second largest city.
Analysts say the Ukrainian operation is developing into a successful counter-offensive.
Kharkiv has been the focus of intense shelling since the 24 February invasion.