'No militant activity'
Ging added that these were his "own staff, senior, experienced, long-serving staff".
"I am very confident now that there was no militant activity inside the school nor militants in the school," he said.
He also reiterated a call for an independent investigation into the incident.
|War crimes: Key facts
The International Criminal Court says war crimes are defined as the violation of the laws and customs of war.
The murder, ill-treatment or deportation of civilian residents of an occupied territory.
The extensive destruction of cities, towns and villages, and any devastation not justified by military necessity.
"If anybody has evidence to the contrary, then let's bring it forward," Ging said.
The Israeli strike on Tuesday left 43 Palestinians dead and about 100 injured.
At least 700 Palestinians have been killed in Gaza and nearly 3,085 wounded since Israel's military offensive began on December 27.
Seven Israeli soldiers and three civilians have died in the same period.
The Israeli army said on Wednesday it stood by its statement issued the day before in which it claimed that mortars had been fired "from within" the school, but then issued another statement later dropping the word "within" to say "mortar fire from" the school.
Chris Gunness, a spokesman for Unrwa, said this was "an extremely important distinction because we have been accused of very serious allegations that our premises were being used to fire rockets".
Michel Abdel Massih QC, a London-based international human rights lawyer, also called for an independent investigation.
"If [Israeli] claims are to be tested properly we need an independent tribunal. The International Criminal Court was set up to deal with these issues, so there is a mechanism for the UN security council to refer the case for investigation," he told Al Jazeera.
When asked if Israel would allow such an investigation, Mark Regev, a spokesman for the Israeli prime minister, said Israel had already held an "initial investigation" which found that troops had returned fire from the UN building.
Regev accused Hamas, the Palestinian faction that controls the Gaza Strip, of committing a "war crime" by using those sheltering in the UN school as "a human shield".
The incident has provoked strong international condemnation with Ban-Ki-moon, secretary-general of the United Nations, branding both the incident and Hamas rocket attacks as "unacceptable".