About 250 people were rescued by the Libyan coastguard on Thursday.
"The Coast Guard patrol spotted a rubber boat carrying more than 100 migrants, 24 miles north of Garrabulli".
And Italy's coastguard said on Tuesday it had rescued 1100 people.
Patrol boat commander Nasser al-Ghammoudi said that the personnel searched for survivors for over five hours after locating the mostly-submerged vessel.
"We've been able to save 60 persons and recovered 31 bodies in the water", said the colonel.
The Italian coast guard, who is coordinating relief and rescue in worldwide waters, have themselves told AFP that other rescue operations were underway on Saturday night.
They had been trying to cross the Mediterranean along with another boat.
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All of the survivors and found were taken to a naval base of Tripoli, where the authorities have provided water, food and medical assistance.
Migrants intercepted or rescued by the Libyans are usually held in detention centres to await repatriation, but waiting times are often long and conditions deplorable.
Almost 3000 migrants are believed to have drowned while trying to cross the Mediterranean this year. In 2015, the European Union witnessed a sharp rise in migrants entering the bloc, many of them refugees fleeing war in the Middle East, Asia and Africa, with Germany receiving almost 900,000 people.
The report said: "Cooperation with Turkey to stem irregular flows is now being replicated with Libya, the main country of departure of migrants smuggled along the central route; however, such an approach is not only morally reprehensible but likely to be unsuccessful, given the context of extremely poor governance, instability and political fragmentation in Libya".
Libya's UN-backed unity government said it would form a "commission to investigate these reports in order to apprehend and bring those responsible to justice". The officials also added that Libya is "a victim of illegal immigration, a transit state, not its source".
However, authorities estimated that less than a third of the migrants arriving in Italy this year are seeking refuge, pointing to an increase in economic migrants, Fargues said.