A 15-year-old boy has been charged with murder, terrorism and other counts for a shooting that killed four fellow students and injured others at a Michigan high school.

Charges against Ethan Crumbley were announced on Wednesday, a few hours after authorities reported the death of a fourth teenager from Oxford High School.

Crumbley is charged as an adult with one count of terrorism causing death, four counts of first-degree murder and seven counts of assault with intent to murder.

Prosecutor Karen McDonald did not reveal a possible motive for the shooting.

She said prosecutors were confident they could show the crime was premeditated, adding: “There is a mountain of digital evidence. Videotape, social media, all digital evidence possible.”

Officers rushed to the school about lunchtime on Tuesday (local time) and arrested the suspect in a hallway within minutes. He put his hands in the air as they approached, Oakland County Sheriff Michael Bouchard said.

Mr Bouchard said the boy’s father had bought the nine-millimetre Sig Sauer used in the shooting last Friday. He did not know why the man bought the semi-automatic handgun, which his son had been posting pictures of and practising shooting.

The four students who were killed were identified as 16-year-old Tate Myre, 14-year-old Hana St Juliana, 17-year-old Madisyn Baldwin and 17-year-old Justin Shilling, who died on Wednesday.

Mr Bouchard said Tate died in a police car as an officer tried to get him to an emergency room.

A teacher who received a graze wound to the shoulder had been discharged from hospital. But seven students ranging in age from 14 to 17 remained in hospital with gunshot wounds, he said.

Undersheriff Mike McCabe said the student’s parents had advised their son not to talk to investigators. Police must seek permission from a juvenile’s parents or guardian to speak with them, he said.

After the attack, authorities learned of social media posts about threats of a shooting at the roughly 1700-student school.

Mr Bouchard said Crumbley had had no previous run-ins with his department, and he was not aware of any disciplinary history at school.

“That’s part of our investigation to determine what happened prior to this event and if some signs were missed, how were they missed and why,” he said.

All schools in the district are closed for the rest of the week.

-AAP