According to Medecins Sans Frontieres (MSF) two rubber boats set off on 1 September, but one of the vessels deflated and sank.
The 276 survivors were eventually taken to the Libyan port city of Khoms, around 100 km (62 miles) to the south-east of the capital Tripoli.
MSF says the group is now being held in “arbitrary detention”.
The survivors, including pregnant women, children and infants, have been treated by MSF for pneumonia or burns from leaked fuel.
Over 1,500 migrants have died while attempting to cross the Mediterranean so far this year, according to the International Organization for Migration (IOM).
Many more have been rescued, although Italy, a primary destination for migrants travelling from Libya, has recently started to refuse entry to migrant ships.
