The boat sank near the island of Bardaa, according to the Libyan Coast Guard.
Around 60 people are estimated to have been on board the boat. Ten people managed to swim ashore and save themselves. Fifty people are feared dead or missing, and a search and rescue operation is underway.
The boat accident is the latest in a series of fatal accidents that often occur off the coast of Libya.
More than 800 people are reported to have died at sea across the central Mediterranean between January 1 and May 16 this year.
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