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A gunman who killed three people at Michigan State University had a history of mental illness and used to lie about having a firearm, his father has said.

The dad told US media his son hid a gun in his room after he was banned from carrying firearms in the wake of a 2019 weapons violation.

After Monday night's rampage the suspect was found dead from a self-inflicted gunshot wound.

The victims were Arielle Anderson, Brian Fraser and Alexandria Verner.

Five others were injured in the attack inside an academic building and the student union.

The gunman's motive remains unclear, say investigators. He had no apparent connection to the Michigan campus in East Lansing, about 90 miles (145km) west of Detroit.

Police identified him as 43-year-old Anthony Dwayne McRae. He was charged in 2019 with a felony for carrying a concealed weapon without a permit.

A police officer in Lansing, Michigan, had seen him sitting outside an abandoned building and asked if he was carrying a weapon.

During a pat-down the officer discovered the loaded semi-automatic pistol, which was registered to the suspect.

He spent a year and a half on probation, during which time he was not permitted to own a firearm.

Michael McRae said his son, who had been living with him in Lansing, bought a gun after the weapons charge, but would not admit it to his father.

"He never let me in the room to show me the gun," the dad said to the Washington Post. "If he showed it to me, I would have put it in the garbage."

The father said that when he heard gunfire in the backyard and challenged his son about it, he would claim it was fireworks, even though bullet casings were on the grass.

The dad said his son "began to change" and became embittered after the death of his mother from a stroke in 2020.

"He began to really let himself go," said Mr McRae. "His teeth were falling out. He stopped cutting his hair. He looked like a wolf man."

Mr McRae told US media he had urged his son, who had trouble holding down a job, to go to a doctor and tried bringing him to church.

A Democratic congresswoman for Michigan, Debbie Dingell, on Tuesday echoed calls by other lawmakers from the Midwestern state for red-flag laws.

Such legislation allows a court order to confiscate firearms from people if they are believed to be a danger to themselves or others.

The attack took place on the eve of the fifth anniversary of a school shooting in Parkland, Florida, that claimed the 17 lives.