The statement came as investigators released police reports and emergency call recordings involving the August 25 shooting of Charles Vacca at the Last Stop range in Arizona.
The police reports name the child's parents as Alex Gen and Alison MacLachlan and do not list the couple's home town.
New Jersey-based lawyer Kevin Walsh said the family "prayed day and night that (Vacca) would survive his injury, and they continue to pray for his family during this terribly difficult time".
The police reports say immediately after the shooting, the girl said she felt the gun was too much for her and had hurt her shoulder.
Her relatives were focused on the girl and did not immediately realise Mr Vacca had been shot.