|Migrants arrive at Tripoli port after they were rescued by Libyan coast guards in the Mediterranean Sea, Libya, January 15, 2018. REUTERS/Hani Amara|
The group includes eight Pakistanis, one of whom called officials to say that smugglers were holding him in a locked room with other survivors.
Previously, just three people were known to have survived after a boat carrying more than 90 people sank off the western Libyan town of Zuwara.
The bodies of 12 Pakistanis who died in the incident have been recovered and brought to a morgue in the capital, Tripoli, awaiting repatriation.
The victims are mostly from Gujrat in northern Pakistan, according the embassy official, who asked not to be named because he was not authorised to speak to the media.
A total of 32 Pakistanis are believed to have been on the boat, and the number who died is still unclear, he said.
Libya is the main gateway for migrants trying to cross to Europe by sea, though numbers have dropped sharply since July as Libyan factions and authorities - under pressure from Italy and the European Union - have begun to block departures.
Zuwara was a top departure point until a local backlash against smuggling in 2015.
So far this year, just over 3,500 migrants are recorded to have crossed from Libya to Italy, about 60 percent fewer than during the same period last year, according the Italian Interior Ministry.
Pakistanis are the third largest national group, after Eritreans and Tunisians.
Pakistanis resident in Libya for decades, many working in the gold business, have tried to leave because of the collapse in the value of the Libyan dinar and a severe liquidity crisis. Others have found their way to Libya through smuggling networks.