Fierce clashes overnight shook the northern port city and sporadic fighting continued on Monday morning, with fighters firing machineguns and rocket propelled grenades.
Tension between the Alawite and Sunni communities in Tripoli has been fuelled by the unrest in neighbouring Syria, where Assad is seeking to crush a 14-month-old uprising which began with largely peaceful protests but has become increasingly militarised.
Assad is from the Alawite sect, an offshoot of Shi'ite Islam, while Syria's revolt has been led by Syria's majority Sunni Muslims.
A small Alawite minority is concentrated in Tripoli, a conservative Sunni city where many residents have been enraged by the Syrian government's crackdown on the mainly Sunni revolt.
Clashes began late on Saturday, and three people were killed over the weekend in the city's Alawite enclave and surrounding Sunni Muslim neighbourhoods.
The fighting in Tripoli, 70 km (43 miles) from Beirut, highlights how sectarian tensions in Syria can ignite conflict in Lebanon. Buildings in the area are still riddled with bullet holes from similar clashes earlier in the year.
Among the deaths at the weekend was a soldier hit by sniper fire. Sporadic fighting also took place between armed Sunnis and the Lebanese army near a main Sunni district, and many of Tripoli's main intersections were blocked by burning tyres.
Prime Minister Najib Mikati, a Sunni Muslim from Tripoli, met religious leaders in the city on Sunday in an attempt to defuse the situation, and local leaders were due to meet later on Monday for more talks to calm the tension.
Tension in Tripoli had been on the rise since last week when Sunni Islamists held a sit-in to protest the arrest of a man who Lebanese authorities said had been in contact with an unnamed "terrorist organisation".
Islamists say Shadi al-Moulawi was arrested because he was working with Syrian refugees.
A statement by al-Jamaa al-Islamiya, an Islamist group in Tripoli, criticised the arrest as lacking due process. Police said he was arrested after thorough surveillance.