The survivors, who included four women and a child, spent two days holding onto what remained of their punctured vessel before they were pulled to safety, said navy spokesman Ayoub Kacem.
Seven bodies were recovered from the surrounding waters, 12 nautical miles off Sayad, about 40 kilometres west of Tripoli, he said.
But the number of lives lost could be much higher as it was unknown how many migrants were originally on board the vessel, he added.
Those rescued were in "critical condition" and suffering from hunger, thirst, fatigue and sunburn, said Kacem.
Another 2,300 migrants were rescued off Libya and two others were found dead today in operations carried out by the Italian coastguard and commercial ships in the area.
It came as the bodies of 35 migrants, including at least 10 children, were being brought to Italy after they fell off an overloaded vessel that was hit by a huge wave while being rescued by an aid boat.
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