“The shooter was engaged by MNPD (Metropolitan Nashville Police Department) and is dead,” a police statement said.

Initial findings suggested she was in her teens but US media reports later said she was 28. Her identity is currently unknown.

She had two assault-type rifles as well as a handgun and gained access to the school through a side entrance, police said. It was unclear whether she had any connection to the establishment.

The three adults killed were employees of the school, which is a private Christian institution. The children were taken to hospital but then pronounced dead.

A mother told US television that her daughter had messaged her that she and her classmates had been hiding in the closet during the incident.

Nashville is the capital of the state of Tennessee - home to just under 700,000 people.

Shootings and mass killings are a common occurrence in the United States but mass shootings carried out by women are extremely rare.

There are more guns in circulation in the US than anywhere else in the world.

“It is ripping our communities apart, and ripping the very soul of this nation,” President Joe Biden told reporters on Monday.

Last May, an 18-year-old gunman killed 19 children and two teachers at a primary school in Uvalde, Texas, before being shot dead by police. In 2012 a gunman killed 20 children and six staff at the Sandy Hook elementary school in Connecticut.

Biden has repeatedly called for stricter gun laws and has tightened regulations under his control slightly in the past.

After the latest tragedy, White House press secretary Karine Jean-Pierre said: “We need to do something. Once again, the president calls on Congress to do something before another child is senselessly killed in a preventable act of gun violence. Again, we need to do something.”

But Congress is against radically limiting access to guns because many lawmakers and the Supreme Court say it is a constitutional right, although some on the left say the wording of the 18th Century document has been misconstrued.