Rescuers managed to save 144 of the migrants and were still searching for others after their vessel overturned 80 miles (128 kilometres) off the Libyan coast.
The total number of passengers on the boat and their nationalities was not yet known.
Late Sunday, the Italian coastguards said they had rescued a total of 2,782 people over the weekend from the Mediterranean, with the good weather prompting an increased number of migrant boats to set off for Italy.
The number of migrants entering the EU illegally in 2014 almost tripled to 276,000, according to Frontex, nearly 220,000 of them arriving via the Mediterranean.
The chaotic situation in Libya has sparked a rise in migrant boats setting out for Europe from its unpoliced ports carrying refugees fleeing conflict and poverty in the Middle East and Africa.