Survivors told local media that 41 migrants died in a shipwreck off the island of Lampedusa, Italy.
A group of four people who survived the disaster told rescuers that they were on a boat that had set off from Sfax in Tunisia and sank on its way to Italy.
The four survivors, originally from the Ivory Coast and Guinea, reached Lampedusa on Wednesday.
More than 1,800 people have lost their lives so far this year in the crossing from North Africa to Europe.
Local public prosecutor Salvatore Vella said he had opened an investigation into the tragedy.
The survivors – a 13-year-old boy, two men and a woman – told rescuers that they were on a boat carrying 45 people, including three children.
They said the boat, which was about 7m (20ft) long, left Sfax on Thursday last week, but sank within hours after being hit by a big wave. Only 15 people are understood to have been wearing lifejackets, but this apparently failed to save their lives.
The Italian Red Cross and German charity Sea-Watch said the four managed to survive the shipwreck by floating on inner tubes and lifejackets until they found another empty boat at sea, in which they spent several days drifting before being rescued.
The four survivors arrived in Lampedusa suffering from exhaustion and shock, but the doctor who treated them, Adrian Chiaramonte, said they had only minor injuries.
“What really struck us was the story of the tragedy,” he said.
“They said they had encountered a first ship, which had apparently ignored them.
“An hour later they were spotted by a helicopter, and an hour after that sighting, they were picked up by an oil tanker.”
The Italian coast guard reported two shipwrecks in the area on Sunday, but it is not clear whether this vessel is one of those.
The United Nations migration agency, the International Organization for Migration (IOM), said the migrants would have had little chance of survival.
“Sub-Saharan migrants [leaving from Tunisia] are forced to use these low-cost iron boats which break after 20 or 30 hours of navigation. With this kind of sea, these boats capsize easily,” IOM spokesman Flavio Di Giacomo told AFP.
Tunisian authorities say Sfax, a port city about 80 miles (130km) from Lampedusa, is a popular gateway for migrants seeking safety and a better life in Europe.
In recent days, Italian patrol boats and charity groups have rescued another 2,000 people who have arrived on Lampedusa.
Tunisia has seen a wave of racism against black Africans in recent months and attempts to leave the country by boat have increased.
The United Nations has registered more than 17,000 deaths and disappearances in the central Mediterranean since 2014, making it the most dangerous migrant crossing in the world.
Last month, the EU signed a $118m (£90m) deal with Tunisia in a bid to curb “irregular” migration.
The money is to be spent on efforts to stop smuggling, strengthen borders and return migrants.
Italy’s far-right government has adopted a policy that forces rescue ships to dock at ports further away, rather than letting them disembark rescued migrants in Lampedusa or Sicily.
It says the aim is to spread arrivals across the country, but NGOs say the policy reduces the amount of time they can patrol areas where shipwrecks are more common. Source: BBC News