The U.N. refugee agency UNHCR said in a statement more than 80 were feared drowned.
Tunisian fishermen rescued four people but one later died in hospital, the UNHCR said.
“The status quo cannot continue,” Vincent Cochetel, UNHCR Special Envoy for the Mediterranean, said in a statement.
“Nobody puts their lives and the lives of their families at risk on these desperate boat journeys unless they feel they have no other choice. We need to provide people with meaningful alternatives that stops them from needing to step foot on a boat in the first place.”
Some of the four initial survivors told the Tunisian coast guard on Thursday that the boat had sunk off the town of Zarzis, Red Crescent official Mongi Slim told Reuters.
A government source said that some of a group of African migrants who were rescued nine miles off the town of Zarzis had informed coastguards that they had set out from Zuwara in Libya, and that dozens had drowned.
At least 65 migrants heading for Europe from Libya drowned last May when their boat capsized off Tunisia.
Libya’s west coast is a main departure point for African migrants hoping to reach Europe, though numbers have dropped due to an Italian-led effort to disrupt smuggling networks and support the Libyan coast guard. Although the fighting in Libya has made the situation more difficult for people-smugglers, international aid officials have warned that it could also prompt more Libyans to flee their country.
Libyans who are picked up by the Libyan Coast Guard are routinely brought back to Libya and detained. The United Nations has pleaded with Libya’s government to free the detainees, some of whom have been locked up for years.
In May, 108 migrants and refugees were sent to the Tajoura detention centre near Tripoli, which was hit by air strikes on Tuesday night, killing at least 53 people.