Motive 'combination of factors' in Wisconsin school shooting, police ...

"At this time, identifying a motive is our top priority," he said. "But at this time it appears that the motive was a combination of factors."

"We are asking anyone who knew her or who may have insights into her feelings leading up to yesterday to please contact the Madison-area Crime Stoppers."

Police are looking into the suspect's social media as part of the investigation.

Chief Barnes said investigators are also talking to students at Abundant Life Christian School to understand whether bullying could have been a factor.

The condition of the injured victims has not changed since Monday night. There are two people in hospital in a life threatening condition and two in stable condition. Another two have left hospital.

The two victims who were shot dead were a teenage pupil and a teacher. None of the victims have been named by authorities.

Madison Mayor Satya Rhodes-Conway said that officials will share information when they can.

"It is absolutely none of ya'lls business who was harmed in this incident," she said during a heated exchange following reporter's question during the press conference.

"Please, have some human decency and respect for the people who lost loved ones or were injured themselves or whose children were injured."

Chief Barnes on Tuesday also clarified that a 911 call reporting the shooting came from a second-grade teacher and not a second-grade student, as was previously stated.

He apologised for the error and said he misread a police log about the incident.

He also said that there were numerous schools in the area that had been targeted by hoax threats, known as swatting, on Tuesday morning. Police do not believe there are any current threats to those schools.

"As a community, we must not allow violence or any act of violence to define us," he said.

"We refuse to allow hate, destruction to win in this city, but rather we will honour our survivors, our victims, through love and support in the Madison way."