Oakland County Sheriff Michael Bouchard told a news briefing hours after the rampage at Oxford High School that investigators were at a loss to explain what might have precipitated "an unspeakable and unforgivable" act of violence.

The suspect, disarmed and taken into custody by sheriff's deputies minutes after Tuesday's shooting began, has declined to speak with investigators after his parents retained a lawyer and denied authorities permission to interview their son, Bouchard said.

"The person who's got the most insight on motive is not talking," the sheriff told reporters.

Bouchard said he was unaware of any previous run-ins with law enforcement by the suspect, in his second year of high school, adding there was "nothing to suggest that there had been disciplinary issues or problems with him at school".

The bloodshed unfolded around midday in Oxford, Michigan, north of Detroit, as terrified students and teachers taking cover inside the school flooded the county emergency dispatch centre with more than 100 calls for assistance, authorities said.

Bouchard credited swift action by his deputies, who he said arrived on the scene in minutes and moved straight toward the sound of gunshots, with preventing a much higher casualty toll.

They confronted the young suspect advancing down a hallway toward them with a loaded weapon, when he put his hands over his head and surrendered, Bouchard said.

The precise sequence of events during the violence remained unclear, but police believe the boy carried the weapon into the school in a backpack, the sheriff said.

Police will ultimately turn over the findings of their investigation to prosecutors, who would decide what charges to bring and whether the suspect would be charged as an adult or a juvenile, the sheriff said.

Three students died in the shooting spree - a 16-year-old boy who succumbed to his wounds en route to a hospital in a patrol car, and two girls, aged 14 and 17, authorities said.

Of the eight others struck by gunfire, seven were students, two of them hospitalised with gunshot wounds to the head.

At least two girls, aged 14 and 17, were described by Bouchard as critically wounded with chest injuries, one of them placed on a ventilator.

A teacher was also treated for a shoulder wound and later discharged.

Undersheriff Michael McCabe said earlier that 15 to 20 rounds were fired during the rampage, which lasted no more than five minutes.

Responding to the shooting, US President Joe Biden said, "my heart goes out to the families enduring the unimaginable grief of losing a loved one".

The latest in a long series of US school shootings will likely fuel debates about gun control and mental health care, with many states allowing easy access to firearms while mental health disorders frequently go untreated.

Australian Associated Press