"The blood of Haddad will not be shed in vain," Obeidah said. "We will punish the killers and we will not allow anyone to hide behind the cloak of any security agency."
Haddad's death comes after another Hamas commander was killed in violence in Bait Hanun on Sunday.
Family feud
But the Preventive Security force in Gaza said the matter was a family feud and that the officer was not on duty, saying the gun battle started after members of a Gaza City family tried to recover a stolen car.
Passengers in the car were members of a Hamas armed group and opened fire on the Preventative Security force, the group said, confirming that one of its members was wounded in a shooting incident.
There has been sporadic fighting between the two groups since their leaders reached a power-sharing deal last month.
Shortly after the shooting, Abbas and Ismail Haniya, the Palestinian prime minister and a Hamas leader, met in Gaza City to try to arrive at a consensus candidate for the post of interior minister.
The interior minister oversees some security forces and disagreements over this appointment have held up the formation of a government.
The meeting ended without agreement on a candidate, but the two sides agreed to continue consultations.