Police in the US state of Wisconsin say the emergency call they received over Monday's school shooting came from a child no older than seven or eight years old.

A teenage pupil and a teacher were shot dead and six others injured at a Christian private school by a 15-year-old girl, named by authorities as Natalie Rupnow. The attacker, who attended the school, was also found dead with a handgun.

The police chief in the city of Madison said the child who rang 911 just before 11:00 local time (17:00 GMT) was in the second grade. "Let that soak in for a minute," Shon Barnes told reporters.

The attacker's motive is not yet clear. The next police press conference is expected on Tuesday afternoon.

The victims have not yet been named, and nor has the child who raised the alarm.

Chief Barnes said two students were facing life-threatening injuries. Four others were taken to hospital and two of them later released.

The attacker, who also used the first name Samantha, is believed to have died from a self-inflicted gunshot wound. No officers fired shots.

She attended the school before launching Monday's attack, Chief Barnes said. The shooting was confined to a study hall with students in mixed grades.

Asked about some text posted online that is purported to have been authored by Rupnow, Chief Barnes said: "We haven't been able to verify that it's authentic. We're certainly aware that it's been posted and the person who posted it alleged to have a connection." Information has been shared with the FBI, he added.

Rupnow's family has been co-operating with the investigation. Local media reported that a property north of Madison was raided on Monday.

Authorities have also asked to hear from witnesses, and a number of those present during the assault at Abundant Life Christian School have spoken to local media.

Nora Gottschalk, aged eight, told CNN affiliate WISC that she was getting ready for lunch when the shots rang out. She saw a teacher who was injured screaming for help. "I was really scared and I was really sad," she said.

Adler Jean-Charles, who is in sixth grade, said he heard two gunshots when he was in English class. "Some people started crying and then we just waited until the police came," he told WISC.

Bethany Highman, who attended the school and now has a daughter who is a pupil, told another CNN affiliate, WMTV: "I pray with my kids every morning that this won't happen, and it's the world we live in."

The school's director of relations said pupils' training for a mass shooting would have been "very fresh" after sessions were held earlier this year.

President Joe Biden said the shooting was "shocking and unconscionable", and called on lawmakers to act immediately on legislation that could prevent more gun violence.

Mass shootings are common in the US, including at schools. According to news organisation EducationWeek, 38 of them have caused deaths or injuries this year. There were a total of 69 victims - including 16 deaths - before Monday's attack.

But school shootings by female attackers are rare.

The school, which has around 400 students from kindergarten to high-school age, remains closed during the investigation.