The fighting intensified on Monday, witnesses and the Lebanese National News Agency reported, a day after the violence began, when supporters of Sheikh Ahmad al-Assir opened fire on an army checkpoint.
The clashes are linked to the ongoing violence in Syria, which has raised sectarian tensions in Lebanon and led to sporadic outbreaks of fighting throughout the country.
Witnesses said gunfire and the sound of shelling had increased in the early hours of Monday morning in the Abra neighbourhood on the eastern outskirts of Sidon, where the fighting is now concentrated.
Lebanon's National News Agency also reported "fierce clashes between the Lebanese army and supporters of Sheikh Ahmad al-Assir."
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An army spokesman told AFP that 12 soldiers had been killed since the fighting began on Sunday, and medical sources reported at least 35 wounded, mostly civilians.
A Salafist cleric told AFP that his bodyguard had been killed on Sunday as they attempted to reach the fighting to negotiate a ceasefire.
Assir's brother told AFP that the cleric and his supporters were inside Abra's Bilal Bin Rabah mosque, where Assir preaches.
"Sheikh Assir will stay in the mosque until the last drop of blood."
"The army is fighting at the moment a few metres" from the mosque, the National News Agency said.
The clashes began on Sunday afternoon, when supporters of Assir, a Salafist cleric known for his opposition to Lebanon's powerful Hezbollah movement opened fire on an army post in Abra.
Assir and his supporters have often accused the Lebanese army, which draws its members from across the country's sects, of backing Hezbollah and its allies and turning a blind eye to their arms.