The private rescue ships Ocean Viking and Sea-Watch 3 have found safe havens.
The Ocean Viking with around 550 boat migrants on board is allowed to dock in Sicily.
The Italian authorities assigned the ship to the port of Pozzallo in the southeast of the island, as the organization SOS Méditerranée announced on Saturday.
Previously, some migrants had already been allowed to go ashore for medical reasons.
According to the aid organization, there were last 118 minors on the Ocean Viking, 94 of them unaccompanied.
The crew had previously rescued the migrants from distress in the central Mediterranean.
Most of the migrants leave the coasts of Libya or Tunisia to reach the EU.
The boats are often overcrowded.
Before the permission to moor the Ocean Viking, the Sea-Watch 3 from the Berlin-based organization Sea-Watch was allowed to head for the port of Trapani in western Sicily with more than 255 boat migrants.
According to the helpers, many migrants are exhausted or show signs of psychological problems.
The number of boat migrants is increasing
A few days ago the two ships called Malta and Italy to assign them a safe harbor immediately.
A spokeswoman for SOS Méditerranée described the situation on board the Ocean Viking as "intolerable".
The people suffered from the high waves and the oppressive heat.
Many are seasick and dehydrated, and some have been burned.
As Malta usually refuses to allow aid ships with migrants on board to enter its territorial waters and ports, Rome was asked to assign the ships a port.
According to the Interior Ministry in Rome, around 29,500 boat migrants reached Italy this year, more than twice as many as in the same period last year and a good seven times as many as between January and July 2019.