Al Jazeera's Ashraf Amritti, reporting from the Gaza Strip, said that Iyad al-Hayya, the nephew of Khalil al-Hayya, a prominent Hamas leader, was among the dead.
Amar Mosbeh, a senior leader of Hamas's military wing, was also killed.
The Izz al-Din al-Qassam Brigades blamed "members of the fugitive party" - a term which usually refers to the Fatah movement of Mahmoud Abbas, the Palestinian president.
"We have information that some elements are planning to carry out bombings against the interests and leaders of Hamas in order to sow anarchy," Khalil al-Hayya said.
Medical officials expect the death toll from the explosion to rise, Amritti reported.
"I looked around the city after the explosion to see what measures Hamas [is taking]. We have been stopped at a number of security checkpoints. They are checking everybody's vehicles and ID," he said.
"The Israeli army has denied to Al Jazeera that they had any role in this attack."
Hamas took full control of the Gaza Strip in June 2007, after forcing out security forces loyal to Abbas.
Earlier, one person was killed and four others wounded by a bomb that went off outside a Gaza City cafe.
The explosion was followed by a second blast near a Hamas politician's house.
The cafe, which was badly damaged, has been targeted in the past, emergency services and police said.
Witnesses blamed "gunmen" for the attacks, suggesting the involvement of rival Palestinian factions.