Police received the first emergency calls from the high school in the town of Oxford, about 40 miles (65km) from Detroit, at 12:51 local time (17:51GMT).

Within minutes, more than 100 calls had been placed to emergency services.

Officials say the suspect surrendered five minutes after police were called when officers confronted the teenager in school corridor.

No shots were fired during the arrest, and the suspect was not injured, police said, adding that he was carrying a semi-automatic handgun that still contained seven rounds of ammunition at the time.

The precise sequence of events remains unclear, but police said they believed the youth had carried the weapon into school in a backpack, and had emerged from a bathroom brandishing the gun,

Three students died in the attack, two girls, Madisyn Baldwin, and Hana St Juliana, and Tate Myre, who died in a local deputy's car before the officer could get him to the hospital.

More than 32,000 people have signed an online petition to rename the school's stadium after Tate, who was one of Michigan's most promising young American footballers.

Two of the injured were undergoing surgery, while the other six were in a stable condition with gunshot wounds. A teacher whose shoulder had a graze wound had been discharged from hospital.

Oakland County Sheriff, Mike Bouchard, said that investigators were at a loss to explain what might have precipitated "an unspeakable and unforgivable" act of violence, adding that the suspect was not co-operating with authorities.

"The person that's got the most insight and the motive is not talking," he told reporters.

The boy had been told by his parents not to talk to police and officers were searching his home, police said.

All schools will be closed for the rest of the week and crisis support is being offered to students and parents.

"Of course I'm shocked. I'm devastated," said Oxford superintendent of schools Tim Throne.

According to the Detroit Free Press newspaper, rumours had been circulating of a possible attack, and some students had decided not to attend classes on Tuesday.

Parent Jody Job told the paper that her son had skipped school because "he felt like something was going to go down".

Robin Redding told the Associated Press that her son had also missed classes due to concerns about safety.

"He was not in school today," she said. "He just said that 'Ma I don't feel comfortable. None of the kids that we go to school with are going today.'"

Police cautioned against speculating on the safety concerns before the investigation is complete.

President Joe Biden spoke about the shooting during a visit to Minneapolis, Minnesota.

"My heart goes out to the families enduring the unimaginable grief of losing a loved one," he said.

US shootings on school grounds have been ticking steadily upwards in recent years, according to pro-gun control group Everytown.

After a brief dip last year during coronavirus lockdowns, the number of such attacks has rebounded with 138 incidents of gunfire on school grounds so far in 2021.