Some of the four initial survivors told the Tunisian coastguard on Thursday the boat sunk off the town of Zarzis, Tunisian Red Crescent official Mongi Slim told Reuters news agency.
A boat carrying at least 86 migrants and refugees capsized off the coast of Tunisia and many are feared drowned.
Tunisian fishermen came across the sinking boat and were able to pull the four survivors out on Wednesday night, but could not find any of the other passengers, said Lorena Lando, head of the International Organization for Migration in Tunisia.
Eighty-two people are now missing in the incident, which come a day after a deadly air attack on a Libyan detention centre killed at least 44 migrants.
Al Jazeera’s Sarah Khairat, reporting from a refugee camp in Zarzis where the survivors were brought, said the vessel was heading from the west of Libya to Europe when it capsized. The four survivors were all men – three from Mali and one from the Ivory Coast.
The Ivory Coast national later died and two of the other men are in hospital.
Slim told DPA news agency that the boat had set sail from Libya on Monday.
Earlier this week, another boat from Libya made it to the Tunisian port of Sfax with 65 people on board.
Libya is one of the main transit countries for migrants and refugees fleeing war and poverty as they try to reach Europe.
The war-torn country has become a hub for human trafficking and migrants often leave for Europe in vessels that are not seaworthy.
Last year, there were 924 deaths. The peak came in 2016 when 2,911 people died during the crossing.