Small arms, machine guns and rocket-propelled grenades were used by the combatants in the Bab al-Tabbaneh and Jabal Mohsen neighborhoods, The (Beirut) Daily Star reported.
They started fighting Sunday in a conflict tied to the Syrian civil war, the Star said.
Many residents in Jabal Mohsen support Syrian President Bashar Assad and much of Bab al-Tabbaneh backs the rebels fighting against Assad's regime, the report said.
Soad Mohammad, Sayed Antoun and Ahmad Sabih, were killed by gunfire during the clashes, officials said.
A number of residential buildings and stores were damaged.
Last month, 30 people were killed and more than 200 injured in similar clashes, the newspaper said.