"I lost Wael ... but I found him hiding in a falafel shop. I'm trying to find my father to take us back home."
Palestinian police tried to calm children at the scene. After news of the shooting spread, hundreds of parents went to Gaza City's Shifa hospital.
After the incident, Fatah supporters tried to close Palestine Street, which has nine schools on it, shouting: "God help us take revenge against the killers."
Later, they drove towards the parliament buildings, firing guns and waving Fatah flags as they called for the Hamas-led legislative council to resign.
Elsewhere in the city, other Fatah supporters were blocking off main roads with burning tyres. Some have called for a general strike.
While Gaza has regularly suffered violence, a direct attack on children is unprecedented.
Tension in Gaza has heightened in recent weeks after Mahmoud Abbas, the Palestinian president, raised the possibility of calling early parliamentary and presidential elections.
Many in the Hamas-led government have said Abbas does not have the authority to dissolve parliament.
The European Union and the US suspended all direct aid to the Palestinian government after the Hamas-led administration was elected in March.