Iman al-Hams, 13, was shot 20 times on 5 October as she walked past an Israeli military outpost on the way to school in Rafah, a refugee camp on Gaza's border with Egypt.
The area has seen much violence during the four-year-old Palestinian intifada.
"Israeli soldiers stormed the area, the girl left the bag and tried to run," Umar Abu Khalifa, 25, a Palestinian witness who lives nearby, said on Monday.
"Bullets hit the [girl's] bag and then soldiers opened fire on the girl."
An Israeli military sources said: "The soldiers fired warning shots into the air. The figure dropped the bag and fled. The soldiers had no way of knowing it was a girl. The soldiers then fired at and hit the figure.
"The outcome was grave and regrettable."
Coup de grace
But Israeli media, quoting unnamed soldiers at the scene, disputed the official military explanation and said the girl was shot at close range with the outpost commander even delivering a "coup de grace" to ensure she was dead.
The army says it thought the girl
may have been sent by fighters
"There was a lot of shooting, but I did not take part. To me it [the figure fired at] looked like a girl," a soldier, whose identity was withheld, said on Israel's Channel 2 television.
A military source said an inquiry into Hams' death was under way but "it is too early to speak of criminal charges".
Lieutenant-General Moshe Yaalon, the chief of army staff,
told Israeli ministers on Sunday that troops at the outpost believed the girl had been sent by Rafah fighters to lure them
outdoors so they could be picked off by snipers.
Human rights groups regularly accuse Israeli troops of excessive force against Palestinians in the occupied West Bank and Gaza Strip and say few abuses are prosecuted.
Hams' family had little faith in the Israeli inquiry.
"We demand the prosecution of Iman's killer, [but] we do not
trust the Israeli judicial system," the girl's older brother,
"My sister was an innocent little girl."
Olive harvest shooting
Elsewhere, an Israeli soldier shot and critically wounded a Palestinian farmer on Monday during a clash over an olive orchard, witnesses said.
The attack appeared to signal that violence would again accompany the West Bank olive harvest this year.
Israeli settlers often harass
Palestinians picking olives
Over the past four years of Israeli-Palestinian fighting, Jewish settlers have increasingly confronted Palestinians picking olives.
Hani Shadda, 26, was shot in the neck by a soldier after troops arrived at the orchard to break up a fist fight between Jewish settlers and the Palestinians picking olives, said Munir Darwish, a Palestinian who was picking with Shadda.
Military officials originally said a settler fired the shot, but later said the facts of the incident were unclear.
Israeli police said four settlers were detained for questioning regarding the fight.
Local Palestinians say Jewish settlers cut down about 1000 olive trees in the Nablus area during the harvest season last year, as part of an effort to drive the Palestinians off their farmland.