"The Fatah Central Committee holds the Hamas movement fully responsible for the victims of the military parade (that was held) among civilians," the committee said in a statement.
Hamas earlier said the explosion at its rally in the northern Gaza refugee camp of Jabaliya was caused by an Israeli airstrike.
Israel denied involvement in the blast, the first deadly incident in the territory since it completed its Gaza pullout.
Fatah's Central Committee slammed Hamas for holding a rally in the densely populated camp, where thousands watched the parade procession attended by dozens of fighters, armed with
rifles and other weapons.
The massive blast on Friday ripped through the Jabaliya refugee camp as throngs of people celebrated Israel's recent withdrawal from the Gaza Strip, just hours after Israeli troops shot dead three Palestinians in the West Bank.
Medical sources said 19 people were killed with more than 80 wounded. Among the casualties were children and resistance fighters.
Among those hurt, 20 were in serious or critical condition, Muawiya Hassanein, head of the Palestinian emergency services in the Gaza Strip, told AFP.
Palestinian security sources put the death toll at 19, but there was no immediate confirmation from medics.
Accusations from a Hamas spokesman that the explosion was caused by rockets fired from an Israeli drone were categorically denied by the Israeli military.
The jeep was ferrying men from the Islamist movement's armed wing to the open space earmarked for the festivities, when it exploded, sending mangled body parts of fighters, children and bystanders flying.
The explosion occurred just as a main leader of Hamas, Ismail Haniya, was to address the swell of activists and supporters.
The blast occurred just as Hamas
leader Ismail Haniya was to talk
The crowd panicked and tried to escape as others tried to provide first aid before the ambulances arrived.
The jeep was partially destroyed and a plume of white smoke spluttered out of its burnt, bloodied wreckage.
"There was smoke all over, and then we saw people in pieces, but we couldn't make out what really happened," said Hazem Abu Rashad, 18.
Witnesses said many children were among the dead and
wounded. Hamas said six of its fighters were among those
killed, including Jihad Shaleal, the head of the military wing in Jebaliya.
The Palestinian interior ministry and witnesses said the blast appeared to have been caused by Hamas explosives inside the car.
"There is absolutely no excuse to parade weapons in the
streets," Palestinian National Security Adviser Jibril Rajoub said on Friday.
"They (resistance groups) are merely trying to express their power and their capabilities. I would hope Palestinian society will soon be rid of all of these images."
"They (resistance groups) are merely trying to express their power and their capabilities"
Palestinian National Security Adviser
Abu Rashad, who was just metres from the explosion, said three fighters with two homemade rockets were in the truck's bed. Three or four other fighters, who are extremely popular with children, rode inside as teenagers thronged the vehicle, he said.
The Palestinian Interior Ministry issued a statement calling on Hamas "to shoulder its responsibility for these ... explosions instead of making accusations against others".
If an accident, the explosion would be only the latest in a string of deadly mishaps.
Six people were killed earlier this month in Gaza City when a Hamas weapons warehouse exploded. Hamas claimed it was an Israeli attack, but an investigation by Palestinian security officials said the blast was an accident caused by the fighters.
During an Islamic Jihad rally at the abandoned settlement of Netzarim last week, a fighter died after accidentally shooting himself in the head.
After the blast on Friday, seven or eight fighters stood in the back of another pickup truck as it drove through the streets of Gaza, using their feet to stop a half dozen rockets from bouncing around in the bed.
A wounded Palestinian being
taken away from the blast site
Hamas spokesman Sami Abu Zuhri told AFP "an Israeli drone fired several rockets at a convoy of cars participating in the parade, creating a large number of martyrs and injured. This is an abominable Israeli crime."
Speaking to Aljazeera, Hamas representative in Beirut Osama Hamdan said tens of Palestinian have seen with their own eyes the Israeli missiles falling down, and expressed dismay over the official statements issued by the Palestinian Authority which attributed the matter to an explosion resulting from "internal error" just minutes after the incident.
"The missile attack is yet another evidence to Israeli total disregard to the Palestinian blood in the absence of an official stance defending it. It is also an indication that although Israel has been defeated on the ground in Gaza, it still has control over the air and sea," Hamdan said.
Hassan Yousof, another Hamas leader, also expressed surprise as to how the Palestinian Authority rushed to adopt the Israeli version and reject the testimonies of tens of Palestinians who saw the missiles coming from the Israeli spy planes.
"The Israeli missiles have targeted leaders of Ezzedine al-Qassam Brigades and political leaders in Hamas," he said.
A Hamas spokesman said the rockets and Qassam missiles exhibited during the military parade were actually "plastic models" as can be seen by anyone close enough or by zooming a camera on any of the missiles.
Hamas's Nizar Rayan showed an
electric device as proof of attack
Hamas leader Nizar Rayan exhibited an electric device picked from the debris which he said was proof of an Israeli missile attack.
An Israeli army spokeswoman said "the Israeli military denies any involvement in the incident".
Hamas has stepped up the number of its military parades since Israel left Gaza on 12 September after a 38-year occupation, although all such events are to end in Gaza on Saturday under an agreement with Palestinian leader Mahmud Abbas.
Rockets fired from the Gaza Strip rained down on the town of Sderot in southern Israel early on Saturday wounding five Israelis, Israeli military sources said.
No fewer than 21 rockets were fired at Sderot, the sources said, in what was the biggest attack of its kind since the Israeli withdrawal from the Gaza Strip.