Thirty people, including five soldiers, were wounded in the shooting between gunmen in Bab al-Tabbaneh and the adjacent neighbourhood of Jebel Mohsen on Saturday, medical and security sources said.
Several people were shot and wounded in separate incidents in Tripoli this week.
Lebanon's caretaker Prime Minister Najib Mikati held talks with the interior minister and other security officials in the Mediterranean city to discuss how to end the violence, which erupted despite the deployment of soldiers in both rival districts.
Sniper shots and rocket fire could still be heard in the area at around 2.30 pm, four hours after the fighting broke out, residents said.
Clashes between fighters in Bab al-Tabbaneh and Jebel Mohsen have flared several times in recent months, killing dozens since the beginning of the year.
In the Bekaa Valley, the Lebanese army said it defused three 107-millimetre Grad rockets on Friday near the north-eastern town of al-Qaa near the Syrian border. It said the rockets were ready for launching when they were discovered.
RA/SHI