Cannito said the child was "in extremely good condition" and had been taken to University Medical Center in Las Vegas for examination.
Cannito said the area where Cole was found was being treated as a crime scene, but gave no information about how Cole got there or where he had been kept since his Wednesday morning abduction.
The child was kidnapped at gunpoint by men who tied up the boy's mother and her boyfriend and ransacked their home.
Cole's father attended the news conference wearing a T-shirt with his son's photograph, but would not comment on when he planned to see his son.
"This is just about Cole being home," Robert Puffinburger said as he choked back tears. "Cole's back."
Authorities arrested Cole's grandfather Clemens Tinnemeyer late Friday in connection with the boy's disappearance. The Las Vegas Review-Journal reported that Tinnemeyer was Cole's maternal grandfather.
Police believe that the abductors were Mexican drug dealers and that the kidnapping at gunpoint was a "message" to Tinnemeyer, 51, whom they said may have stolen millions of dollars from dealers.
Tinnemeyer was arrested in Riverside, Calif., and was being held in nearby San Bernardino on a material witness warrant issued by a federal court in Nevada.
Officer Cris Johnson, a Las Vegas police spokesman, declined to say what role Tinnemeyer played in the drug operation or whether the kidnappers had been seeking a ransom.
Police believe methamphetamine was involved, Johnson said.
Las Vegas police didn't know Saturday whether Tinnemeyer had a lawyer. He was scheduled to appear before a federal magistrate Monday in Riverside.
Authorities investigating the abduction were also focussing on two other men, including a Mexican citizen identified as Jesus Gastelum.
Gastelum, who is in his mid-30s, is believed to be in Las Vegas or Southern California, police said. The other "person of interest" was not identified.
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