Authorities declined to release details of any conversation that the 15-year-old had with investigators, but they said he was the Griegos' son. The sheriff's office said he is charged with two counts of murder and three counts of child abuse resulting in death.
The sheriff's office said it wouldn't release any further information about the case until Sheriff Dan Houston holds a news conference Tuesday morning.
On Sunday, a police roadblock cut off public access to the narrow dirt road that leads to the home, which is surrounded by trees and an agricultural field on one side.
Neighbors said they saw the first police cars and ambulances arrive at the home Saturday night. The road was blocked and word of the shootings began to make its way through the neighborhood.
Peter Gomez, a 54-year-old carpenter who lives about 200 yards from the home, said he had seen the family — a husband and wife and their four children — pass by many times but didn't know them personally.
"It's a horrible thing," Gomez said. "You see all this stuff that happens all over the country, the shootings in the schools and theaters, and then it happens right here. It's sad."
Associated Press writer Jacques Billeaud in Phoenix contributed to this report.