It was not immediately clear what prompted the shootout in the Ein El-Hilweh camp, where gunfights are common between armed groups jockeying for power.
Monday's confrontation involved gunmen from the militant Asbat Al-Ansar group, which is on a US terrorism list and which Washington has accused of being linked to Al-Qaeda.
An official said one of the militants shot a Fatah member, igniting the clash with other gunmen from the mainstream Palestinian movement. His account could not immediately be confirmed.
Two bystanders died and a Fatah member was seriously wounded, said the officials, who spoke on condition of anonymity because they were not authorized to make official statements.
The echo of gunfire and rocket-propelled grenades reverberated in the camp and in the nearby city of Sidon. Some families in the teeming camp fled to safer areas.
Ein El-Hilweh is home to 70,000 people, making it the largest of Lebanon's 12 Palestinian refugee camps. It is notorious for gunbattles and tit-for-tat bombings between rival groups.
A number of fugitives live in the camp, which is under Palestinian jurisdiction and off limits to Lebanese authorities. Among the fugitives are members of Asbat Al-Ansar, or Band of Partisans.
