"A resident of the Jabal Mohsen district and a passer-by caught in crossfire were killed on Wednesday in clashes that also wounded 32 people," the official said.
"The wounded belong to both the Sunni and Alawite rival camps."
He said that forces were ordered "to increase patrols, arrest anyone who threatens the public security even if the use of force is necessary".
Panicked residents were forced the scene of the fighting as rivals fought with rockets, sniper rifles and grenades. Several roads were blocked and local shops and schools were closed, according an AFP correspondent.
One Tripoli resident, who asked not to be identified, told a local news agency: "All of a sudden hell broke loose."
Fractious region
The road separating the two districts was the site of sectarian fighting two weeks ago that left nine people dead and 45 injured.
Officials told the AFP news agency that fighting broke out at about 9.20pm (18:30 GMT), beginning with some explosions. The clashes intensified and subsided within an hour.
However, witnesses said that at about 4.30am (0130 GMT) on Wednesday morning rockets and machine gun fire could be heard.
Bab al-Tabbaneh is a majority Sunni area were locals largely support the government.
The majority of Jabal Mohsen back the Syrian and Iranian-backed opposition from the Shia Muslim Alawite sect.
A statement issued after the meeting stressed the "need for calm".
"The army and security forces should play their role on the ground," it said. "A party is working to cause sedition between the two sects."
Fighting in May in different parts of Lebanon had raised the spectre of civil war. The battles in Tripoli two weeks ago was the worst violence seen since that time.
Political parties are currently working to form a government of national unity, part of a deal brokered in Doha, the Qatari capital, on May 21.
Disagreement over government posts has prevented the government from being formed so far.