Montague also is accused of stabbing his sister-in-law, a mentally disabled woman, more than 20 times with a point of the ax before bursting out of a home into the street.
"We don't know what set him off," Roberts said after Montague was interviewed by homicide detectives and taken to the Clark County jail.
"He claims he blacked out. He said he doesn't remember anything," Roberts said.
The boy was found dead in the street, near where his stroller was found overturned.
His mother was taken to Sunrise Hospital and Medical Center in very critical condition with what Roberts said were disfiguring face and head injuries.
Their names weren't immediately made public.
The sister-in-law, whose name and age also weren't released, was reported to be in fair condition at University Medical Center in Las Vegas.
Neighbors saw the attack and shouted at Montague to stop while calling 911, Roberts said.
Montague left the ax in the single-family home before police arrived, and scuffled with officers who tried to use a Taser to subdue and arrest him, said Officer Bill Cassell, a department spokesman. One police officer received what Cassell said were minor injuries that did not require medical treatment.
Montague was being held without bail on charges of murder, attempted murder and attempted murder of a police officer pending a court appearance Tuesday morning. Court officials said it was not immediately clear if he had a lawyer.
Montague was described as the caregiver for his sister-in-law, who Roberts said was stabbed repeatedly in torso, stomach and legs.
Roberts said Montague's wife was at work and two children were in the house during the attack. Another child was at school. The children weren't hurt.
