The vessel went down in the Mediterranean two days ago, just hours after launching from the Libyan town of Zuwara.
Fishermen saw four people clinging to pieces of wood and alerted Tunisian authorities. One of the four survivors later died at a hospital. The Red Cross says the boat was carrying too many people.
One of the survivors says the boat started filling with water while the migrants could still see lights on the shore. An urgent telephone call for help went unheeded because the caller was unable to tell Libyan rescuers the exact location of the boat.
The survivor says he and the three others were in the water for two days before the fishermen found them.
The sinking came on the same day an airstrike hit a migrant detention center outside Tripoli, killing 44.
The United Nations and human rights groups have decried treatment of mainly African migrants who try to escape poverty and violence by fleeing to Europe from Libyan shores.
Many picked up at sea are taken back to Libya and held in poor conditions in detention centers. Private rescue boats operated by charities have found themselves unwelcome in key European ports.