The clash in the town of Khan Yunus early on Thursday disrupted a tenuous peace that had been in place since Mahmoud Abbas, the Palestinian president and Fatah leader, and the Hamas-led government of Ismail Haniya, began talks last week to try to end violence in Gaza.
Fatah and Hamas traded blame over who began Thursday's gun battle.
Fatah sources said its fighters were ambushed by Hamas men.
Hamas said one of its fighters opened fire after his home came under attack.
Hamas crushed the long-dominant Fatah in January elections, but since taking power in March the group has faced a Western aid blockade on Gaza and the Israeli-occupied West Bank.
Sworn to Israel's destruction, Hamas has resisted pressure from abroad and from Abbas loyalists to accept Israeli-Palestinian peacemaking.
Palestinian poverty, deepened by the Western aid embargo, has spread discontent that occasionally spills over into violence.
At least 10 people have been killed in clashes between Hamas and Fatah supporters since March, prompting fears among some Palestinians of a possible civil war.