The move brings an apparent end to the days-long saga after about 500 migrants were held offshore by authorities.

They had been rescued by charity ships last month during crossings from North Africa to Europe.

All 213 migrants on the Geo Barents will be allowed to leave the vessel, Doctors Without Borders (MSF) said on Tuesday evening.

Prime Minister Giorgia Meloni has said she wants to stop people traffickers "deciding who enters Italy".

Her right-wing government has been criticised for denying safe port to the rescue boats.

MSF tweeted on Tuesday evening that following an "assessment of vulnerability" conducted by health authorities, all those on the Geo Barents would be allowed to disembark.

Speaking from on board the vessel, MSF's Riccardo Gatti said: "We are really happy to receive the information from the health authorities that finally all the survivors that we have on board will be disembarked soon. We hope tonight.

"This is really the ending of the rescue operation," he said.

Earlier, 89 people on board the Rise Above had been allowed ashore.

Chiara Cardoletti, the UN refugee commissioner's representative in Italy, said that Italy had been on the front line of the migrant crisis for too long and she called on the European Union to find a common strategy.

"We appreciate what Italy has done by allowing boats to enter territorial waters, allowing children, women and people with medical problems to disembark," she told the BBC. "Italy cannot be left alone, the European Union must step forward and find appropriate and faster solutions."

On Monday, three people leapt into the water from the Geo Barents after being refused permission to disembark in the Sicilian port of Catania. They were among about 250 migrants told to remain on two boats in Catania after officials deemed them "healthy".

Mission Lifeline, a German charity that runs the Rise Above, said in a statement that it was "relieved that the rescued people are finally safe on land" at Reggio Calabria on the Italian mainland, a few kilometres from Sicily. Many of the 89 who disembarked were described as minors.

Authorities told Italian media that they had been allowed to leave because they had been picked up in a so-called save and rescue (SAR) incident in the Mediterranean, whereas those on the two boats docked in Sicily were not.

The charity condemned what it called an "undignified political game" that had kept them at sea. The crew of the Rise Above have not yet been able to leave the boat, according to Italian reports.

Mission Lifeline said the Rise Above was by far the smallest of the three vessels in port and its passengers had suffered badly in recent heavy seas.

Italy is one of the main entry points into Europe. Since the start of the year, 85,000 migrants have arrived on boats, according to the UN.

Migrants set sail in small, overcrowded boats from North Africa, often get into distress and are rescued by charity vessels.

Over the weekend, two boats docked in Sicily, carrying a large group of migrants.

Most were allowed to leave, but 35 men on the Humanity 1 and another 215 on the Geo Barents, which is run by MSF, were told they would have to stay on board.

According to Italian media reports, a fourth boat, Ocean Viking, run by French charity SOS Mediterranée, is on its way to France where it will be allowed to dock. The vessel has some 234 migrants aboard, who were picked up from the sea off Libya 17 days ago and have repeatedly demanded access to an Italian port.

SOS Mediterranée said the situation on board Ocean Viking had "reached a critical limit" that required an immediate response.

"We are facing very severe consequences, including risks of loss of lives. Physical and psychological wellbeing of survivors and crew have been exhausted by over two weeks of blockage at sea," said Xavier Lauth, the group's director of operations.

Both SOS Humanity, which runs Humanity 1, and MSF have argued that everyone on board their ships is vulnerable, as they were rescued from the sea.

SOS Humanity is also taking the Italian government to court, alleging that a decree by an Italian minister, allowing the migrants to be kept on the ships, breaks both Italian and international law.