Heavy fighting between gunmen in the port city of Zououara, near the Tunisian border on Tuesday killed four people and left several more wounded, AFP reported.
The people of Zououara are mostly Berbers, who participated in the fight against the Gaddafi regime. But this city is surrounded by Arab communities, some have supported Gaddafi last year.
But according to the ruling National Transitional Council (NTC), at least 10 people were killed and 45 injured in the towns of Regdalin and Jamil.
An interior ministry official told Reuters the confrontation had started on Sunday when a group of Zuwara men hunting for game accidentally shot someone from Al-Jumail.
On Monday, Libya's Prime Minister, Abdurrahim El-Keib, visited Sunday in Sebha, some 750 km south of Tripoli where clashes between rival militias left 147 dead and nearly 400 wounded during the past week. The clashes were the deadliest since the fall of the regime of Muammar Gaddafi last year.
El-Keib said he wanted to show the rival camps in Sebha that there is enough room for all tribes and all ethnic communities there. "We announce that reconciliation efforts have resulted in an agreement for a cease-fire," said El-Keib, adding "the calm prevailing now in Sebha."
"The situation is now calm and the forces under the Ministry of Defense control strategic areas in the city including the airport," said the chief of staff Youssef al-Mangouch during a joint press conference.
Months after the fall of Muammar Gaddafi, Libya is still the scene of almost daily clashes between squabbling tribes and militias.
El-Keib's government has been unable to secure the country as it lacks a viable security force as interior ministry has struggled to impose its authority on dozens of brigades comprising of former rebels who fought against Gaddafi’s forces and who now have become a law unto themselves.