Sources at the Ayn al-Hilweh camp, south of Beirut, said the local headquarters of Yasser Arafat's Fatah movement and a Fatah checkpoint were attacked by Islamic militants.
Correspondents say tension has been high at the camp since last month, when Fatah and other groups helped the Lebanese army to arrest a wanted Islamic militant, Badih Hamade, who is accused of killing three army intelligence officers.
In the past two weeks alone, there have been four bomb attacks against Fatah targets in Lebanon.
Violent skirmishes are commonplace in the camp, but according to Lebanese officials Tuesday's clashes were the worst in more than a decade.
Street fighting
Security sources said the attackers belonged to the militant Dunniyeh group, who have been hiding in Ayn al-Hilweh for more than two years after they clashed with troops in northern Lebanon.
The attackers sprayed automatic fire and threw grenades at Fatah positions, killing one fighter.
Fatah guerrillas then fired back, killing one of the Islamists.
The exchange of fire reportedly lasted for nearly an hour, damaging several houses, wrecking cars and knocking down water pipes in the shanty town.
Khaled Aref, a Fatah official, said the various Palestinian groups had decided to issue a warning to the militants to surrender or be arrested by force.
"We agreed to issue a warning to the members of this group to hand themselves over. If they don't we are determined to arrest them by force and hand them over to the Lebanese state," Mr Aref said.
But Abu Ramez Sahmarani, a member of the Dunniyeh group, insisted that the militants would never surrender.
"We will not hand over ourselves to those infidels and we will not leave the camp even if there is a bloodbath," he said.
Wanted militants
Ayn al-Hilweh, home to some 75,000 refugees, is largely controlled by the various Palestinian factions inside.
Although the Lebanese authorities guard the gates, they rarely enter the camp.
Several leaders wanted by police are thought to be hiding in the camp. One of them, Abu Mohjen, the leader of the Asbat al-Ansar group, is on a US list of terror organisations.