"We spent seven to nine minutes waving the flags, and our faces were looking at them [the soldiers]," HRW quoted the girls' grandmother as saying.
"And suddenly they opened fire and the girls fell to the ground."
Two of the incidents in question have also been investigated by the BBC.
In five of the seven incidents, Israeli soldiers shot at civilians who were walking down the street with white flags, trying to leave the areas of fighting, HRW said.
"All available evidence indicates that Israeli forces were in control of the areas in question, no fighting was taking place there at the time, and no Palestinian forces were hiding among the civilians or using them as human shields," the report said.
The Israeli foreign ministry has opened investigations into at least five cases involving Palestinians who were waving white flags.
As of the end of July, one case had been closed. The Israeli military said troops had fired at "suspicious men" who ignored warnings as they walked near a Palestinian family carrying a white flag.
Sadly, Hamas terror operatives ruthlessly pervert the intent of the IDF's obligations to prevent harm to civilians by exploiting those with white flags as cover for belligerent action and to protect themselves from return fire
HRW said its findings were based on site investigations, ballistic evidence found at the scene, medical records of victims and lengthy interviews with multiple witnesses.
An Israeli government spokesman said the report lacked credibility because it was based on evidence from an area under Hamas control.
The Israeli military said troops were obliged to respect white flags, but accused "Hamas terror operatives" of "exploiting those with white flags as cover for belligerent action and to protect themselves from return fire".
But it gave no details of specific incidents.
Israel has said its soldiers acted lawfully during the operation, although some mistakes were made, such as the bombing of a house containing 21 civilians by accident.
It says it went to great lengths to distinguish between civilians and combatants, while Hamas put civilians at great risk by firing rockets from near schools and UN facilities, commandeering hospital facilities and ambulances, hiding weapons in mosques and booby trapping civilian neighbourhoods.
War crime accusation
Human Rights Watch last week accused Hamas of war crimes, for firing rockets at Israeli population centres.
Israeli spokesman Mark Regev on white flag claims
The group also says Palestinian militants operated from populated areas.
HRW's Bill Van Esveld said last Thursday that a Newsweek report quoted in a recent Israeli Foreign Ministry briefing was "as clear evidence of human shielding [by Hamas] as you're going to get".
Journalist Rod Nordland wrote on 20 January: "Suddenly there was a terrific whoosh, louder even than a bomb explosion. It was another of Hamas' homemade Qassam rockets being launched into Israel - and the mobile launch-pad was smack in the middle of the four [apartment] buildings, where every apartment was full."
But Mr Van Esveld said he was only aware of evidence of "three or four" such cases, and had seen more evidence of the use of human shields by Israeli troops than by Palestinian militants.
The Israeli activist group Breaking the Silence has published anonymous testimonies of Israeli soldiers describing a procedure in which they said Palestinians were forced at gunpoint to enter building where militants were hiding.
Israel said its 22-day operation in Gaza was "necessary and proportionate" and was aimed at reducing Palestinian rocket fire.
The Israeli military says it his currently investigating about 100 incidents, of which 13 are criminal investigations.
On Wednesday a soldier was jailed for seven months for using a credit card he stole from a Palestinian in Gaza during the operation to withdraw money in Israel.
Israel says 1,166 Gazans died in the conflict. Palestinian human rights groups put the figure at 1,400. Accounts differ as to how many were civilians. Thirteen Israelis died, including three civilians killed in Palestinian rocket attacks.
Israel says 12,000 rockets and mortars were fired at Israel between 2000 and 2008 - nearly 3,000 in 2008 alone.
Hamas denies committing war crimes and firing rockets from residential areas.
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