Eight of them were killed on the weekend when the violence flared in Sebha, some 600 kilometers south of Tripoli, the source said, adding that 18 others were wounded in the clashes.
On Saturday, the rival tribes fought for the control of an ancient hilltop citadel that overlooks Sebha, a region known for its smuggling routes.
Sebha, where tribal rivalries have frequently spilt over into bloodshed, has been rocked by violence since February.
The fighting is pitting the Arab Alwad Suleiman tribe against the Tubus, who are repeatedly accused by their detractors of including foreign fighters, namely from Chad, in their ranks.
Since the beginning of May more than 31 people have been killed and 121 wounded in the tribal clashes, the medical source said speaking on condition of anonymity.
Libya has been gripped by chaos since a NATO-backed uprising toppled and killed longtime dictator Muammar Gaddafi in 2011, with rival administrations and multiple militias vying for control of the oil-rich country.
A UN-backed unity government based in the capital Tripoli and headed by Sarraj has struggled to assert its authority outside the west, and military strongman Khalifa Haftar controls much of the east.
