Survivors from a boat that sank off Libya's coast on Tuesday said about 50 people who had embarked with them were missing and feared dead.

Libyan coast guard vessels picked up about 300 migrants from three boats off the coast of the North African country on Tuesday, but one of the boats foundered and the coast guard only found 16 survivors.

"We found the migrant boat at about 10 o'clock this morning, it had sunk and we found 16 migrants. The rest were all missing and unfortunately we didn't find any bodies or (other) survivors," said Nasr al-Qamoud, a coast guard commander.