The explosion went off on Friday evening under a car parked near a beach in Gaza City. Islamic group Hamas said three of its members died on the spot along with a young girl, and that two other members were fatally wounded and died soon afterwards. More than a dozen bystanders were injured.
The media reports said Hamas, which blames the attack on Fatah, has carried out searches of more than 40 buildings in Gaza containing Fatah offices.
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.
Senior Hamas official Mahmud al-Zahar told a crowd of supporters gathered for a funeral of the victims on Saturday that police have information on who was responsible for the attack.
Friday's bombing was the worst attack in the impoverished Palestinian enclave since Hamas and Israel agreed on a truce mediated by Egypt in June.