Eight bodies were found and 35 migrants rescued on Tuesday and Wednesday, Seddik al-Jayach, an official in Zuwara, told AFP on Thursday.
Survivors had clung onto the sinking vessel for five days before it ran aground on the Libyan coast, he said.
Survivors had told Jayach that the sunken ship had been carrying between 120 and 130 asylum-seekers, including women and children, from different African countries.
The Libyan navy said the shipwreck occurred off the coast of Sabratha, a town west of Tripoli that is a hub for asylum-seekers heading for Europe and from where the vessel had set off.
Last week, Libya’s coastguard rescued more than 3,000 asylum-seekers aiming to make the perilous crossing from the Mediterranean Sea to Europe, while Italy picked up another 2,000.
The tally was the highest reported out of Libya for a one-week period since a dramatic fall in numbers in mid-July.
The European Union has reportedly given tens of millions of euros to Libyan authorities to try to stem the flow of asylum-seekers.
Officials say the funds have mainly been used to strengthen Libya’s coast guard, reinforce its southern border and handle those transferred to detention centers.
The United Nations International Organization for Migration (IOM) says more than 130,000 asylum-seekers have arrived in Europe by sea since the start of 2017.
This number is less than half the number for 2016. Three-quarters of the new arrivals in 2017 landed in Italy. The rest of the asylum-seekers set foot in Greece, Cyprus and Spain.
Asylum-seekers are usually packed into flimsy rubber boats with barely enough fuel to get them to their destination.
Some 2,500 asylum-seekers lost their lives attempting to make the perilous voyage across the Mediterranean Sea this year. During the same period in 2016, 3,200 asylum-seekers had lost their lives, according to the UN agency.