The Italian coast guard ship, Diciotti, has arrived in the Sicilian port of Catania with 932 migrants and two bodies on board.
A further rescue ship is waiting off the coast of Libya for instructions on where it should go.
The Diciotti was part of seven operations organised by the European Union to pick up migrants from the Mediterranean Sea on Sunday.
En route the Diciotti dropped off some people in Lampedusa who required urgent medical attention. They included pregnant women and a minor.
The operation comes at diplomatically difficult time in Mediterranean politics with Italy and Malta turning the Aquarius, with 600 migrants on board, away from their ports.
The vessel near Libya belongs to the German NGO, Sea Watch, and is facing similar difficulties. It has 41 survivors of a shipwreck on board along with the bodies of 12 migrants.