Margaret McEwan died from a single air rifle pellet wound in the accident in the front room of her cousin's house in Bedworth, Warwickshire. Police confirmed that Margaret's parents, Elaine and Thomas, were in the room at the time.
Detective Inspector Graham Moreton said: "Margaret and her parents were visiting this family. It was a social call and the children were playing. As a result of the boy handling the weapon in some way, Margaret received the injury to her chest." She was taken to hospital but died later.
Mr Moreton refused to confirm the identity of the cousin, who was earlier named by other officers as James McEwan.
He told a news conference: "The inquiry is progressing very slowly. The reason for this is that the witnesses are all severely traumatised. We have to balance our need for information with their welfare."
He said of the cousin: "This boy is a juvenile and he is really suffering. We have not been able to interview him so far because he is so traumatised. He is very distressed and has been seen by medical staff."
The weapon involved in the shooting at the house in Blair Drive, Goodyer's End, Bedworth, was a BSA Sportsman .22 single-pellet air rifle.
"It belonged to a member of the family and was quite old," said Mr Moreton.
"I understand it was usually used for target practice. I believe generally it was stored very responsibly and the implication of it being an accident is that no one knew it was loaded."
Margaret, a pupil at the Newdigate First School in Bedworth, lived with her family in Ashington Road in the town.
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