Three children and three staff members were killed in a shooting in a school in the US' Tennessee state on Monday morning.

The shooter -- a 28-year-old girl -- was "engaged" by law enforcement officers and killed. She was carrying two "assault-type rifles and a handgun", as per police.

The shooting took place in a private Christian school in Nashville that runs from preschool through to the sixth grade.

White House Press Secretary Karine Jean-Pierre said President Joe Biden has been briefed on the school shooting.

The police got the first calls sometime past 10 am Central Time. "The police department response was swift," police spokesperson Don Aaron told reporters.

"They heard shots coming from the second level. They immediately went to the gunfire. When the officers got to the second level, they saw a shooter, a female, who was firing. The officers engaged her. She was fatally shot by responding police officers."

There was no official word on the shooter's motivation.

School shootings have become tragically commonplace in the US. Just a few days ago, a 17-year-old was fatally shot after he had shot and wounded two members of the administrative staff of a Denver school.

Sandy Hook Promise, an organization founded and run by family members of the victims of the 2012 massacre at Sandy Hook school in Connecticut, called gun violence and school shootings "a uniquely American epidemic".

Mass shootings, incidents with four or more victims, are even more common. Easy access to deadly weapons is to be blamed chiefly, but gun law reforms have been slow and bitterly contested by a powerful gun lobby.