Sunni and Alawite gunmen have been fighting in the Bab al-Tebbaneh and Jabal Mohsen districts of Tripoli since Monday.
Two of the casualties were Sunnis, said the security official. The third, an Alawite, died after he and an accomplice on a moped opened fire on an army roadblock and he was hit by return fire.
Residents of Bab al-Tebbaneh support the revolt against Syrian President Bashar al-Assad, while those in Jabal Mohsen back Assad. They have fought frequently since the Syrian conflict erupted in March 2011.
The higher Sunni toll is explained by the fact that Jabal Mohsen overlooks much more densely populated Bab al-Tebbaneh and because the Alawites are better organised, security sources say.
The northern port city is 80 per cent Sunni, with Christians and a smaller number of Alawites making up the balance.
Acting Prime Minister Najib Mikati said Saturday that "security forces will take every step to put an end to the violence and chaos" in the city of 200,000. "They will be strict and impartial."
A security official said the army had separated the two sides and pushed them back.
It has prompted residents to flee the impoverished neighbourhoods, and schools and universities have been closed in since mid-week.
Lebanon is deeply divided into pro- and anti-Damascus camps.
The division has widened since Lebanese 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.
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