A total of 89 people on board the Rise Above were allowed ashore.
But people remain on three other rescue boats as Rome vows to halt irregular migrants crossing the Mediterranean.
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.
But Chiara Cardoletti, the United Nations (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. -BBC