The Italian Coast Guard Ship "Diciotti" rescued 86 migrants who survived to the incident, IOM said.
Since trafficking dinghies are often crammed with far more than 100 migrants, fears quickly arose that dozens more could be missing.
Reuters spoke to survivors who say that about 50 people who had boarded the boats now are missing, while Libya's Coast Guard stated in a press release it believes that number might be as high as 100.
"Sixty-four migrants lost their life in the shipwreck [which] occurred last Saturday", Mr Di Giacomo wrote on Twitter, saying "probably 56 missing migrants" perished at sea.More news: Search for MH370 continues, to cost between RM82m to RM280m if found
Sono 64 le vittime del naufragio avvenuto sabato tra Libia e Italia.
The migrants came from Mali, Gambia, Ivory Coast, Sierra Leone, Cameroon, Senegal and Nigeria, he said.
The survivors were taken to a naval base in Tripoli, and many of them said at least 70 people were aboard the boat when it left Khoms, east of Tripoli. Bianco said the child is now with her aunt, who was among the survivors.
Search-and-rescue efforts continued for more than 12 hours in rough conditions, the navy said. "It's a step-by-step process, hopefully they will work through what happened and later provide more information", Agliozzo said.More news: Snow strands thousands of tourists in Switzerland
Some 119,000 embarked on the perilous journey, a decrease of one third on the previous year, according to Italy's interior ministry.
The massive flood of migrants across the Mediterranean over the past few years prompted the European Union to take measures, including training and equipping Libya's coast guard to stop boats attempting the risky sea crossing.
Europe is experiencing a major influx of migrants who have been trying to cross the continent, mostly through illegal means, since the beginning of the Syrian Civil War in 2011 and the spate in the violence casued by the terrorist group, the Islamic State (IS) in Iraq and Syria.More news: Teacher handcuffed after questioning superintendent's $38000 raise during school meeting
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