Last week in the same area, rescuers recovered the bodies of around 170 people after the shipwreck of another vessel carrying illegal immigrants from sub-Saharan Africa.
"During a routine patrol we found 15 floating bodies of African migrants 15 kilometres (nine miles) offshore," coastguard Abdellatif Mohammed Ibrahim told AFP.
"These bodies, including two women and two children, were floating near a ripped inflatable craft," he said.
Other bodies may have sunk in the sea at the location off Al-Qarabole, 60 kilometres east of Tripoli, he said.
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Local officials at Ben Guerdane in southeast Tunisia believe the bodies were from a sinking off the coast of Libya.
They were "probably" some of the people who went missing earlier this week when a boat capsized after leaving the Libyan port of Zwara, heading for Italy, an official said.
Mired in unrest and political chaos, Libya has been a launchpad for illegal migrants trying to reach Europe and who turn to people smugglers to cross the Mediterranean, mainly to Italy.