Another 28 North Africans attempting to sail to Italy are confirmed drowned, according to the Tunisian government.
The boat had 75 migrants - 70 Moroccans and five Tunisians - when it broke into pieces off the town of Chott Meriem, 170 km (100 miles) southeast of Tunis, a few hours after it left Tunisia for Italy on Sunday, they said.
"We recovered 28 bodies so far, seven of them early on Tuesday and 21 later on Sunday and Monday. We rescued 11 people and 36 others are missing," a senior official said.
The deaths come after Italy deported hundreds of immigrants to Libya in recent days as record numbers of would-be asylum-seekers flooded its southern islands, drawing criticism from human rights groups.
The Tunisian government deployed eight ships and an army helicopter to search for the missing passengers.
The 11 rescued were 10 Moroccans and one Tunisian, but authorities had not yet identified the dead.
, eager to maintain good ties with Italy, has stepped up efforts to stop the organised smuggling of illegal migrants across the Mediterranean, with officials saying 163 illegal migrants had been arrested in Tunis and two other towns.
President Zain al-Abidin Bin Ali has urged the coast guard, army and police to step efforts to stem the flow of illegal migration when he summoned the defence and interior ministers to his office on Monday.
Scores of north African Arabs drown each year trying to escape political repression and poverty by attempting to cross the Mediterranean in rickety vessels.