The violence has claimed at least thirteen lives since the weekend. More than 100 people have been also injured as supporters and opponents of Syrian President Bashar al-Assad clashed in the city.
Two Lebanese soldiers were reportedly among the dead.
The soldiers were killed after the Lebanese Army entered the flashpoint area to break up the clashes between residents of rival neighborhoods of Bab al-Tabbaneh and Jabal Mohsen on Tuesday.
Many homes have been destroyed since the breakout of violence on Sunday.
Lebanese Prime Minister Najib Mikati issued a statement on Wednesday saying that the Army has “full authority” to take the necessary measures to put an end to the clashes.
While Bab al-Tebbaneh residents support militants fighting against the Syrian government, the inhabitants of neighboring Jabal Mohsen are loyal to Assad.
Tripoli has been the scene of fierce clashes between the supporters and opponents of the Syrian government since the beginning of the unrest in Syria more than two years ago.
In February, at least three people were injured in clashes between supporters and opponents of the Syrian government in the area.