The inflatable boat was carrying more than 100 people when it went down, according to navy spokesman Ayoub Kacem, who said rescuers had saved just 17 people, including some women.
Survivors clung to the vessel for hours before help arrived.
The boat sank off the city of Khoms, around 100 kilometres (60 miles) east of the Libyan capital, Kacem said.
In another incident, the Libyan navy said it had also rescued 267 migrants of various African nationalities, off Zawiya to the west of Tripoli.
Women and 17 children were among those rescued, said Kacem, who added that bad weather had hampered the operation.
Over the weekend, 10 migrants died and dozens of others, including children, went missing off the Libyan coast, according to aid organisations.
Since the 2011 fall and killing of longtime dictator Moamer Kadhafi, Libya has become a key launch pad for migrants making desperate bids to reach Europe, often on unseaworthy vessels.
Last year alone, 3,116 people died attempting the crossing, according to the International Organization for Migration (IOM), including 2,833 from Libya.
But there has been a sharp drop in crossing attempts since the summer of 2017 following efforts by Italy to discourage migrants from trying to make the journey.
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