The violence has closed schools and sent families into flight, with no sign by Wednesday evening of the fighting dying down.
"Two people have been killed since Monday night. One of them was a 13-year-old child, the other a 32-year-old man," the official told AFP.
In all, 33 people have been wounded since Monday night, when an interview with Assad was being aired on television.
The 13-year-old victim was from Jabal Mohsen, a majority Alawite neighbourhood in the northern port city of Tripoli whose residents support Assad.
The man killed was from Bab al-Tebbaneh, whose Sunni inhabitants support the anti-Assad revolt in neighbouring Syria.
The violence has forced families from both districts to flee their homes for other areas of Tripoli, said an AFP correspondent in Lebanon's second city.
Early on Wednesday, "gunmen from the two sides tried storming each other's districts", said the official. "The army fought them off, in a battle that raged at around 3:00 am (0000 GMT)."
All Tripoli's schools stayed closed on Wednesday because of the violence.
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On Wednesday evening, the two enemy districts continued to see sporadic fighting and shooting.
An AFP correspondent in Tripoli saw black smoke rising from a shop in Bab al-Tebbaneh, which had been burned down.
Violence has frequently broken out in the two impoverished neighbourhoods since the March 2001 start of Syria's uprising.
Meanwhile, the army said it arrested four Syrians on the Wadi Hmeid-Arsal road in eastern Lebanon after they entered the country illegally from Syria.
Their car was laden with "military grade shotguns and pistols, ammunition and military equipment, as well as a number of hand grenades."
Lebanon is deeply divided into pro- and anti-Damascus camps.
The division has widened since Shiite militant group Hezbollah admitted in May it was sending fighters into Syria to support Assad's troops.
Small radical Sunni organisations have also sent men across the border to fight alongside the rebels.
Lebanon was dominated politically and militarily by Damascus for 30 years until 2005.