The violence has closed schools and sent families into flight.
"Two people have been killed since Monday night. One of them was a 13-year-old child, the other a 32-year-old man. Thirty other people have been wounded," the official told AFP on condition of anonymity.
The clashes broke out on Monday night as 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.
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The violence forced families from both districts to flee their homes for other areas of Tripoli, said an AFP correspondent in Lebanon's second city.
Early today, "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."
All Tripoli's schools stayed closed today because of the violence.
Violence has frequently broken out in the two impoverished neighbourhoods since the March 2001 start of Syria's uprising.
Lebanon is deeply divided into pro- and anti-Damascus camps.
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.