The motive was not immediately known but the suspect had drawn detailed maps of the school and left behind a "manifesto" and other writings that investigators were examining, Police Chief John Drake told reporters.

The latest in an epidemic of deadly mass gun violence that has come to routinely terrorise even the most cherished of US institutions unfolded on Monday morning at The Covenant School, whose students consist mostly of primary school-age children.

Drake identified the suspect as a woman by the name of Audrey Elizabeth Hale, 28, a resident of the Nashville area, and referred to the assailant by female pronouns.

In response to reporters' questions the chief said: "She does identify as transgender." Whether the suspect identified as a man or woman was not made clear.

Addressing an early evening news conference, Drake said police were working on a "theory" about what may have precipitated the shooting and would "put that out as soon as we can".

The Metropolitan Nashville Police Department began receiving calls at 10.13am of a shooter at the school, and arriving officers reported hearing gunfire coming from the building's second floor, police spokesman Don Aaron told reporters.

Two officers from a five-member team shot the assailant in a lobby area, and she was pronounced dead by 10.27am.

"The police department response was swift," Aaron said.

Drake said the 28-year-old suspect had previously been a student at the school and had gained entry by firing through one of the doors.

Three students were pronounced dead after arriving at Monroe Carell Jr. Children's Hospital at Vanderbilt with gunshot wounds, hospital spokesman John Howser said in a statement. Three adult staff members were killed by the shooter, police said.

The victims were later identified as Evelyn Dieckhaus, Hallie Scruggs, and William Kinney, all age 9, along with staffers Mike Hill, 61, a school custodian, Cynthia Peak, 61, a substitute teacher, and Katherine Koonce, 60, listed on the Covenant website as "head of school".

Besides the deceased, no one else was shot, Aaron said.

Students' parents were told to gather at the nearby Woodmont Baptist Church to be reunited with their children. Parents trickled out of the building with their youngsters in tow. One woman was visibly distraught as she was escorted alone out of the church to a waiting squad car by police officers who said they were headed to Vanderbilt.

Reacting in Washington to the shooting, US President Joe Biden urged Congress again to pass tougher gun reform legislation and ban assault-style weapons.

"It's sick," Biden said during an event at the White House.

"We have to do more to stop gun violence. It's ripping our communities apart, ripping the soul of this nation."

At the state level, Tennessee in 2021 did away with its permit requirement for carrying a concealed handgun and now allows anyone 21 and older to carry a firearm - either openly or concealed, without a permit - as long as they are legally allowed to purchase the weapon.

Possessing a handgun is outlawed in Tennessee for anybody who has been convicted of a felony offence involving violence or drugs.

The Covenant School, founded in 2001, is a ministry of Covenant Presbyterian Church in the Green Hills neighbourhood of Nashville with about 200 students, according to the school's website. The school serves preschool through sixth graders and held an active shooter training program in 2022, WTVF-TV reported.

Nashville Mayor John Cooper expressed sympathy for the victims and wrote on social media that his city "joined the dreaded, long list of communities to experience a school shooting."

There have been 89 school shootings - defined as anytime a gun is discharged on school property - in the US so far in 2023, according to the K-12 School Shooting Database.

There were 303 such incidents last year, the highest of any year in the database, which goes back to 1970.

Australian Associated Press