A shooting at a private school in the US city of Madison killed a teacher and a student, the city police chief said at a press conference on Monday.

Madison Police Chief Shon Barnes said that the suspected shooter was a 15-year-old female student at the school.

The shooter was pronounced dead when officials arrived at the scene and the shooter died of what is believed to be a self-inflicted gunshot wound, Barnes said. 

The police chief added that a second grade student called 911 around 11 a.m. to report the shooting, adding: "Let that soak in for a minute." 

Officials were still searching for a motive behind the shooting.

Police chief initially declined to name suspected shooter

Barnes did not reveal the gender or name of the suspected shooter during an initial press conference.

But US media outlets, like the Associated Press agency and the New York Times were reporting that the shooter was female.

The police chief maintained that the suspected shooter's family was cooperating with officials and that all remaining children had been reunited with their families.

Barnes said two students remained in critical condition at a hospital and their injuries were life-threatening.

Four people were also injured, he added. Those injuries were not life-threatening and two of those injured people have been released from the hospital.

Biden presses Congress to enact stricter gun laws

President Joe Biden called the shooting "shocking and unconscionable" in a statement Monday. "We need Congress to act. Now," he said.

"From Newtown to Uvalde, Parkland to Madison, to so many other shootings that don’t receive attention — it is unacceptable that we are unable to protect our children from this scourge of gun violence. We cannot continue to accept it as normal," he said.

"Every child deserves to feel safe in their class room. Students across our country should be learning how to read and write — not having to learn how to duck and cover," he added.

School director says students handled themselves 'magnificently'

The Abundant Life Christian School is a private school, attended by some 400 children from Kindergarten to 12th grade.

A school official told reporters at a news conference that students knew very quickly that the situation was not a drill when they were asked to lock down.

The students "handled themselves magnificently," said Barbara Wiers. "When they heard 'lockdown, lockdown,' they knew it was real," she said.

School shootings are not uncommon in the US, with some 322 reported this year alone, according to the K-12 School Shooting Database website.

Such shootings often spark intense political debates over gun control, with many blaming the ease of gun access in the US for the high number of killings at schools.

ab/rc,rm (Reuters, AP)