The fighting erupted on Saturday following an operation earlier launched by Hamas security forces against the members of the Hilles clan affiliated with the rival Fatah faction who the Islamist group believes were behind a series of bombings in the territory last week including one that killed five Hamas members and a girl.
The nine dead included two Hamas policemen while the others were civilians and pro-Fatah gunmen.
Clan leader Ahmed Hilles and 179 of his supporters ran to a border crossing with Israel. An Israeli army spokesman said all of the 180 men were allowed to cross into Israel and the injured among them were taken to Israeli hospitals.
The Gaza Strip has been controlled by Hamas since June last year, leaving Palestinian President Mahmoud Abbas, who leads Fatah, in charge of only the West Bank. The two main Palestinian factions have been bitterly divided since then.