The gun used by a 15-year-old who opened fire at his Michigan high school on Tuesday and killed three pupils was bought by the suspected shooter’s father, police said.

Eight other people were wounded, some critically, in the incident at Oxford High School in Oxford Township, a community of about 22,000 people roughly 30 miles north of Detroit.

Oakland County Sheriff Michael Bouchard said investigators were still trying to determine a motive for the shooting

“The person that’s got the most insight and the motive is not talking,” Mr Bouchard said at a news conference.

The suspect’s father had bought the 9mm Sig Sauer used in the shooting on Friday, Mr Bouchard said, adding that he did not know why the man bought the gun.

The sheriff said the suspect had practiced shooting with the gun and “posted pictures of the target and the weapon” online.

The three pupils who were killed were 16-year-old Tate Myre, 14-year-old Hanna St Julian, and 17-year-old Madisyn Baldwin, with Mr Bouchard saying the boy died in a patrol car as a deputy tried to get him to a hospital.

The sheriff said a teacher who received a graze wound to the shoulder was discharged from the hospital, but seven pupils ranging in age from 14 to 17 remained hospitalised with gunshot wounds, including 14-year-old girl who was on ventilator after surgery.

Undersheriff Mike McCabe said earlier that authorities were aware of allegations circulating on social media that there had been threats of a shooting at the roughly 1,700-pupil school before Tuesday’s attack, but he cautioned against believing that narrative until it is investigated.