Six people are dead after a woman armed with multiple guns went on a rampage in a Christian elementary school in Nashville, Tennessee.

The victims were three school children and three staff. The suspected shooter also died during a shootout with police – bringing the total toll to seven.

The latest US mass shooting happened at The Covenant School, a private Christian school of about 200 students and 50 staff that caters to ages three to 11.

Police who responded to emergency calls at 10.30am Monday (local time) arrived to the sound of gunfire on the second level of the school building.

Heading upstairs to a lobby-like area, a team of five officers met the 28-year-old Nashville woman and there was then a shootout.

The suspected killer, whose identity has not been released, was shot dead by police.

She had been armed with at least two semi-automatic rifles and a handgun, said Don Aaron, a spokesman for Metropolitan Nashville Police Department.

Police said the suspect may have been a former student of the school.

Students are taken to safety as police respond to the Nashville school shooting. Photo: AAP

The three students were pronounced dead after arriving at Monroe Carell Jr Children’s Hospital at Vanderbilt with gunshot wounds.

The victims have not been named or identified.

First Lady Jill Biden was among the first to publicly react to the latest tragedy while at an event in Washington, saying “our children deserve better”.

“We just learned about another shooting in Tennessee. A school shooting. And I am truly without words,” Dr Biden said.

“Our children deserve better. And we stand, all of us, we stand with Nashville in prayer.”

Nashville Mayor John Cooper said his school had joined the “dreaded, long list of communities to experience a school shooting”.

“My heart goes out to the families of the victims. Our entire city stands with you,” he wrote in Twitter.

President Joe Biden said the shooting was “sick”.

“It’s heartbreaking, a family’s worst nightmare, and I want to commend the police who responded incredibly swiftly, within minutes.

“We have to do more to stop gun violence. It’s ripping our communities apart, ripping at the very soul of the nation.

“We have to do more to protect our schools so they are not turned into prisons.”

Female mass shooters are rare, accounting for only four mass shootings since 1966 in the US, as catalogued by The Violence Project.

So far in 2023 there have been 89 school shootings in the US, according to the K-12 School Shooting Database, a website founded by researcher David Riedman.

In 2022, there were 303 such incidents, the highest of any year in the database, which goes back to 1970.

Police outside The Covenant School. Photo: AAP

The Covenant School, founded in 2001, is a ministry of Covenant Presbyterian Church in the Green Hills neighbourhood of Nashville. It has about 200 students, according to its website.

The school serves pre-school through to sixth graders and had held an active shooter training program in 2022, WTVF-TV reported.

Mr Aaron said police were yet to determine a motive.

“We do not know who she is at this juncture,” he said, although earlier reports suggested she “appeared” to be a teenager.

“We now know that there are three students who were fatally wounded as well as three adults inside the school,” he said.

“We are working to identify those victims. Including the shooter, a total of seven persons were killed as a result of this morning’s incident at the school.

Students’ parents were told to gather at a nearby church.

White House press secretary Karine Jean-Pierre called on lawmakers to pass gun safety legislation.

“How many more children have to be murdered before Republicans in Congress will step up and act to pass the assault weapons ban, to close loopholes in our background check system, or to require the safe storage of guns? We need to do something,” she said.