Aquarius, the vessel of Médecins Sans Frontières (MSF), saved 421 migrants, mostly from Eritrea. There is no further information in what European port they will bring the migrants.
Meanwhile the Libyan coastguard has been also conducting sea rescue operations.
More than 200 were rescued on Saturday after their boats foundered off Libya’s western coast, the Libyan navy said.
The coastguard conducted two rescue operations off the city of Garabulli, 60 kilometres (40 miles) east of Tripoli, spokesman Colonel Abu Ajila Abdelbarri said.
He added that patrols had found 31 bodies and 60 survivors from one boat, while all 140 passengers had survived in a second boat.
Migrants from Somalia, Ghana, Ethiopia, Nigeria and four from Pakistan were among those rescued.
Libyan patrol boat commander Nasser al-Ghammoudi said one of the vessels was three-quarters under water when the coastguard arrived.