Survivors, all men, were found clinging to a flotation device
At least 97 migrants were missing after their boat sank on Thursday off the Libyan coast, a navy spokesman said.
Survivors said the missing include 15 women and five children, General Ayoub Qassem told AFP.
He said the Libyan coastguard had rescued a further 23 migrants of various African nationalities just under 10km off the coast of Tripoli.
The boat's hull was completely destroyed and the survivors, all men, were found clinging to a flotation device, he said.
Those who had disappeared were "probably dead," but bad weather had so far prevented the recovery of their bodies, Qassem added.
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An AFP photographer said survivors had been given food and medical care at Tripoli port before being transferred to a migrant centre east of the capital.
Six years since the revolution that toppled dictator Muammar Gaddafi, Libya has become a key departure point for migrants risking their lives to cross the Mediterranean to Europe.
Hailing mainly from sub-Saharan countries, most of the migrants board boats operated by people traffickers in western Libya, and make for the Italian island of Lampedusa 300km away.
Since the beginning of this year, at least 590 migrants have died or gone missing along the Libyan coast, the International Organization for Migration said in late March.
In the absence of an army or regular police force in Libya, several militias act as coastguards but are often themselves accused of complicity or even involvement in the lucrative people-smuggling business.
More than 24,000 migrants arrived in Italy from Libya during the first three months of the year, up from 18,000 during the same period last year, according to the UN High Commissioner for Refugees.