Italy has arrested three men who they believe trafficked up to 200 people aboard a wooden boat that smashed apart on rocks off southern Italy on Sunday, killing at least 64 people, police said on Tuesday.

Lieutenant colonel Alberto Lippolis said a Turkish man and two Pakistani nationals had sailed the boat from Turkey to Italy despite the terrible weather and been identified by the survivors as “the main culprits of the tragedy”.

"According to initial investigations, they allegedly asked the migrants for about 8,000 euros ($8,485) each for the deadly journey,” said Lippolis, commander of a finance police team in the region of Calabria.

“All three have been arrested.” The boat hit rocks and broke up early on Sunday in heavy seas near the town of Steccato di Cutro on the toe of Italy.

Rescuers pulled a dead man from the sea on Tuesday, bringing the number of bodies retrieved so far to 64, including about 14 children. There were 80 survivors, who said that the boat had been carrying between 150 to 200 migrants.

"We will carry on searching ... the sea until we are certain that we have found everyone,” said Rocco Mortato, a member of the underwater diving team of the fire brigade.

The boat had set sail from the port of Izmir in western Turkey towards the end of last week. Rescuers said most of the migrants came from Afghanistan, with the others from countries including Iran, Somalia and Syria.

Pakistan's foreign ministry said 20 of its citizens had been on the boat, and 16 of them had survived but four were missing. The tragedy has fuelled a debate on migration in Europe and Italy, where the recently elected right-wing government's tough new laws for migrant rescue charities have drawn criticism from the United Nations and others.

Italian Prime Minister Giorgia Meloni said in an interview on Monday that she had written to European Union institutions calling for immediate action by the bloc to stop migrant boat trips so as to prevent more deaths.

"The more people depart, the more risk dying,” she told RAI public television.“The only way to tackle this issue seriously, with humanity, is to stop the departures.” Hundreds of thousands of migrants have reached Italy by boat over the past decade, fleeing conflict and poverty back home.

The United Nations Missing Migrants Project has registered more than 20,000 deaths and disappearances in the central Mediterranean since 2014, including more than 220 this year, making it the most dangerous migrant route in the world.