Fighting between Sunni and Alawite residents of the city was continuing for a fourth day today but clashes had become more sporadic, the source told AFP.
An AFP correspondent said large parts of the city of 500,000 people were shut down today, with schools and shops closed after a night of fierce clashes.
Two Lebanese soldiers were among the dead, the source said, and at least 10 of the wounded were military personnel deployed to try to calm the violence that broke out on Sunday.
Clashes have often pitted residents of Sunni Bab el-Tebbaneh against those from the neighbouring Alawite area of Jabal Mohsen.
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Violence has regularly broken out in the city since the beginning of the uprising in neighbouring Syria.
The largely Sunni town is home to a small community of Alawites, an offshoot of Shiite Islam to which Syrian President Bashar al-Assad belongs.
The latest violence began as the Assad regime launched an assault on the rebel stronghold of Qusayr, near the border with Lebanon.