There was no immediate claim of responsibility for the drive-by attack, which left the schoolbags and a small plastic bag with a sandwich covered in blood.
"I have no words. Words stop at the extent of this crime," the boys' father, Baha Balousheh, told The Associated Press. "I am a father who has lost his children."
Senior officials in the intelligence service, which is loyal to the Fatah Party of President Mahmoud Abbas, blamed the Islamic militant group Hamas for the shooting. Balousheh, a Fatah member, was a lead interrogator in a crackdown on Hamas a decade ago. The attack marked the the first time children have been targeted, reports CBS News correspondent Robert Berger from Jerusalem.
Hamas denied involvement and denounced the bloodshed.
While dozens have been killed in Gaza's escalating lawlessness since Hamas defeated Fatah in January parliamentary elections, the death of the children was especially shocking and was likely to trigger widespread confrontations at a time Hamas and Fatah were at loggerheads over the creation of a national unity government.
The shooting has raised fears of a Palestinian civil war, Berger reports.
At midday, thousands of angry Fatah supporters joined a mass funeral procession for the boys that snaked through the streets of Gaza City. Hundreds of Fatah security officers fired their rifles in the air. Fatah activists burned tires, blocked roads and shut down the city's commercial market in protest.
Fatah parliament members issued a statement calling on Abbas to dismiss the Hamas government, "which is pushing us with its policies and programs to civil war."
Abdel Karim Kahlout, Gaza's mufti or top Islamic authority, issued a religious ruling calling for the death sentence against the killers.
"I ask the rulers to carry out an execution against the killers. No punishment is acceptable but execution," he said.
In the attack, gunmen in two vehicles riddled the car carrying the children with some 60 bullets, Palestinian security officials said. Balousheh's three sons — Osama, 9, Ahmed, 6, and Salam, 3 — were killed, in addition to an adult, hospital officials said. Balousheh was not in the car.
The car was soaked in blood. A child's backpack, emblazoned with cartoon characters and the word "Friend," lay on the front seat, covered in blood. Another schoolbag was in the back.
Four more people were wounded in the attack on Palestine Street, which is lined with nine schools. The attack sent children in the area running for cover, some dropped to the ground, others fled in panic.