The latest shooting at an elementary school in the United States was carried out by a 28-year-old former pupil, according to police.

Three of the victims were pupils aged nine or under at Covenant School. Police named them as nine-year-olds Evelyn Dieckhaus, Hallie Scruggs and William Kinney, as well as Cynthia Peak, 61, Katherine Koonce, 60, and Mike Hill, 61.

Police named the gunwoman as Audrey Hale, who they said was transgender and carried out the attack after drawing a detailed map of The Covenant School in Nashville and conducting surveillance of the building.

A man drops flowers to a makeshift memorial where baloons and Teddy bears are left on the outside the Covenant School building at the Covenant Presbyterian Church, in Nashville, Tennessee, March 27. -(Photo by BRENDAN SMIALOWSKI/AFP via Getty Images)

The website of The Covenant School, a Presbyterian school founded in 2001, lists Katherine Koonce as the head of the school since July 2016.

Cynthia Peak was a substitute teacher and Mike Hill was a custodian, according to investigators. Ms Koonce was described as the Head of School on Covenant's website.

The suspect was fatally shot by police 14 minutes after the initial emergency call was made.

Metropolitan Nashville Police chief John Drake did not give a specific motive but gave chilling examples of the planning for the attack.

Suspect Audrey Hale holding an assault rifle at the Covenant School building at the Covenant Presbyterian Church, in Nashville, Tennessee. - A heavily armed former student killed three young children and three staff in what appeared to be a carefully planned attack at a private elementary school in Nashville on Monday, before being shot dead by police. Photo by -/Metropolitan Nashville Police De/AFP via Getty Images

“We have a manifesto, we have some writings that we’re going over that pertain to this date, the actual incident,” he said.

“We have a map drawn out of how this was all going to take place.”

He told NBC News investigators believe Hale had “some resentment for having to go to that school”.

Police said Hale gained entry by firing into glass doors and was armed with two “assault-style” weapons as well as a handgun, two of which were believed to have been obtained legally in the Nashville area.

They added a search of Hale’s home turned up a sawed-off shotgun, a second shotgun and other unspecified evidence.

Rachel Dibble, who was at the church as families found their children, described the scene as everyone being in “complete shock”.

“People were involuntarily trembling,” she said. “The children … started their morning in their cute little uniforms, they probably had some Froot Loops and now their whole lives changed today.”

Speaking at the White House, President Joe Biden called the shooting a “family’s worst nightmare” and implored Congress again to pass a ban on certain semi-automatic weapons.

“It’s ripping at the soul of this nation, ripping at the very soul of this nation,” he said.

The president ordered the US flag to be flown at half-mast on all federal buildings and spoke to Tennessee governor Bill Lee and Nashville mayor John Cooper about the shooting, officials said.

Founded as a ministry of Covenant Presbyterian Church — which is affiliated with the conservative evangelical Presbyterian Church in America — The Covenant School is located in the affluent Green Hills neighbourhood just south of downtown Nashville.

The school has about 200 pupils, as well as roughly 50 staff members.

A statement from the school said: “Our community is heartbroken.

“We are grieving tremendous loss and are in shock coming out of the terror that shattered our school and church.

“We are focused on loving our students, our families, our faculty and staff and beginning the process of healing.”

Nashville shooting: Former pupil kills six in shooting at Covenant School in Tennessee