The motive behind a deadly shooting at a Christian school in Wisconsin appears to stem from "a combination of factors", authorities said on Tuesday.

A teacher and student were killed and several others wounded in the shooting at Abundant Life Christian School in Madison. A further six people were injured, two critically.

The shooter was named by police as 15-year-old Natalie Rupnow who died at the scene from a self-inflicted gun shot wound. She was a student at the school. 

Addressing a news conference, Madison Police Chief Shon Barnes said they were still working to establish a motive. 

"We're looking at multiple factors, including possible bullying," he said. "Identifying a motive is our top priority, but at this time, it appears the motive involves a combination of factors."

The attack unfolded in a mixed grade study hall just before 11am on Monday morning. Police, who were attending training just a few miles away, arrived on the scene within minutes.

The police are investigating Rupnow's cellphone and online activity, and are looking into possible links between the teenager and an apparent manifesto circulating online. 

Police said Rupnow used a pistol to carry out the shooting, but have not confirmed how she came to have possession of the gun. 

Mr Barnes said that Rupnow's parents have been cooperating with investigators. Questions have been raised about whether they may be held legally responsible for the shooting as has happened in other states. 

"We also want to look at if the parents may have been negligent. And that's a question that we'll have to answer with our district attorney's office. But at this time, that does not appear to be the case," Mr Barnes told CNN.

The school has asked for prayers and expressed gratitude to law enforcement: "We are [so] grateful to the totality of the law enforcement community who have been involved in helping us. They have been amazing! We pray God protects and provides for each one as they perform their high calling of public service."