Charles Vacca, 39, was shot in the head on Monday as he showed the New Jersey girl how to fire the Israeli-made 9mm gun. As she pulled the trigger, the gun jumped out of her left hand toward Vacca, who was standing beside her.
"We just want to make sure they understand that we know it was a tragic accident and that it's something that we're all going to have to live with," Vacca's 19-year-old daughter, Ashley, told NBC's "Today" show.
"My heart goes out to the little girl, and I feel sorry for her and for her family," Vacca's ex-wife, Anamarie, told the network on Friday.
The deadly incident occurred at a gun range in Arizona that caters to Las Vegas tourists, many of whom drive an hour from the gambling center to fire high-powered weapons. Ashley said she planned to write a letter to the girl and her family.
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Another daughter, Elizabeth, said: "I wanted to make sure they didn't spend a big portion of their life surrounding it around this one incident."
Authorities in Mohave County in California said the death was being handled as an industrial accident, with state occupational safety and health officials investigating.
An autopsy on Vacca was completed, but the cause and manner of death were pending, said Colleen Pitre, a representative of the medical examiner's office.
Experts say an Uzi can fire five rounds one-third of a second.