Clashes took place in the Abra neighborhood of the port city of Sidon, 40 kilometers south of Beirut, DPA news agency reported Monday.
Witnesses say the sound of machine guns and rockets filled the area, trapping hundreds of civilians in their homes, with some making appeals on local television stations for the army to secure a safe passage for them to leave the area.
The violence prompted the army to bring reinforcements, an army source said.
Violence broke out after al-Assir followers surrounded an army checkpoint in Abra, where a vehicle transporting other supporters of the firebrand sheikh had been stopped by the Lebanese army,
"The clashes are now concentrating near the Bilal Bin Rabbah
Mosque where most of al-Assir's 250 followers are hiding," an army source said.
The army has vowed in a statement that it "will not tolerate" the violence, and that it "will continue to fulfill its mandate to suppress civil strife in the country."
Fifteen people are reported to have been killed in the fighting since Sunday, among them 12 army soldiers. Forty others were wounded, the Lebanese army said in a statement.
Al-Assir is a staunch supporter of Syrian militants fighting against the government of President Bashar al-Assad.