At least five migrants died during the incident including a toddler who was travelling with his mother.
Both the Libyan coastguard and Seawatch were present when the vessel, carrying about 140 migrants capsized and both carried out the rescue.
During the rescue operation, some migrants tried jumping off the Libyan patrol boat which had rescued them to reach the Seawatch vessel a few metres away.
The Libyans tried to discourage the migrants from trying to reach the German boat.
The incident sparked mutual recrimination by Seawatch and the Libyan coast guard.
The tiny body of the toddler was carried off the boat on arrival at the Sicilian port of Pozzallo and placed in a coffin. The child's mother was helped off the ship. Seawatch rescue worker said they had left many bodies in the water in order to rescue the people still alive.
Libya is the main departure point for migrants trying to travel by boat to Europe. But numbers crossing to Italy have fallen sharply since July due to a drop in people smuggling and increased activity by Libya's European-backed coastguard.
