"We believe the 3-year-old had to manipulate the action enough to chamber a live round," Peterson said in a news release.
The boy underwent initial surgery at Logan Regional Hospital before being flown to Primary Children's Hospital, where he died late Friday.
Investigators believe the shooting was accidental but will document the facts and refer the case to the Cache County Attorney's Office for a review, Peterson said.
He said the names of the people involved are being withheld because of the ages of the children and the fact that the case is under investigation.
"This is a stark reminder of the importance of keeping all kinds of weapons out of the reach of children," the release said.
Jocelyn Strauss, regional manager for Moms Demand Action for Gun Sense in America, said about one-third of children in the United States live in households with guns and more than 2 million of them are in homes with unsecured guns. "As an organization, we feel the need to start an honest conversation about what responsible gun ownership means and how we should develop technology and laws that make safe storage the norm," said Strauss, who lives in Tucson, Ariz.
Moms Demand Action is under the umbrella of Everytown for Gun Safety.
Strauss said many children know where their parents hide their guns, which can result in an accidental shooting.
"The parents don't think it can happen to them," she said. "It's easy to believe that your guns are well hidden from your children. Parents really underestimate their children's curiosity."