As well as the three victims, police said the suspect had died apparently from a “self-inflicted gunshot wound”.

Another five people were injured in the attack at the main campus in the city of East Lansing late on Monday.

Police described the suspect as “a black male, shorter in stature”. They later said he was 43 years old with no known affiliation to the university.

Students and local residents were told to “shelter in place” during the manhunt.

Police later lifted the order, saying there was “no longer a threat to campus”. They added the suspect had been found off campus. The identities of the victims have not been released.

In photos released earlier, the suspect was wearing a denim jacket, a navy baseball cap and red trainers.

The shooting started shortly after 20:00 local time on Monday (01:00 GMT Tuesday) and sparked a huge manhunt involving hundreds of officers.

The officers who responded to the attack found victims at the Berkey Hall on the campus’s north side, and the adjacent MSU union building.

Students reported on social media that they were hiding. One — Drew Russ, an 18-year-old from Los Angeles — was watching Star Wars with friends at his dorm when a deluge of text messages arrived.

He and everyone on his floor in the dorm, which is about a mile from Berkey Hall, stayed put, he told MSNBC on Monday night.

“I couldn’t believe this was happening on my college campus,” he said. Another student jumped out of a first-floor window at Berkey Hall, her parents said.

Mike and Natalie Papoulias rushed to the campus on Monday night from Jackson, Michigan, after receiving a call from their daughter, they told local media.

In a text message, the daughter said: “I heard somebody get shot, Mom. It’s terrifying. I could smell the gunpowder.”

A number of ambulances were seen arriving at the scene, and the injured — some believed to be in a life-threatening condition — are being treated in hospital.

“This truly has been a nightmare that we are living tonight,” said Deputy Chief Chris Rozman of the university’s police force.

All campus activities have been canceled for at least 48 hours. East Lansing lies about 70 miles (112km) north-west of Detroit.

The Michigan shooting is the latest in a growing number of college campus shootings in the US.

In November, three members of the University of Virginia football team were killed on campus, while 10 people were killed in a shooting at Umpqua Community College in Oregon in 2015.

In 2007, 33 people were killed in a shooting at Virginia Tech.