The 28-year-old, who was a former student there, was killed by police after a confrontation with officers following the attack at the Covenant School.

The woman was named Audrey Hale and lived in Nashville, sources told NBC News.

Police said Hale was armed with two assault-type rifles and a pistol. They earlier said she appeared to be aged in her teens.

Officers started receiving reports of an attack at 10.13am (4.13pm UK time) and as police began clearing the ground floor of the school they heard gunfire coming from the second floor.

Two officers from a five-member team opened fire in response and fatally shot the suspect at 10.27am (4.27pm).

Detectives say they don't know how the woman got into the school, which teaches students up to sixth grade (around 12 years old).

The three children, who were all students, were pronounced dead after they arrived at hospital.

The female attacker died after being "engaged by" officers, police said in a Twitter post.

Biden condemns 'sick' attack

US President Joe Biden called Monday's attack "sick" and "heartbreaking".

He said the US needs to do more to protect schools and he called on the Senate to pass the assault weapons ban - which would criminalise the knowing sale, manufacture, transfer, possession or importation of many types of semi-automatic weapons and large-capacity magazines.

No one else was shot in the assault.

So far this year, there have been 89 US school shootings - defined as when a gun is fired on school property.

In 2022, there were 303 such incidents, the highest of any year in the K-12 school shooting database, which goes back to 1970.

Read more:
US mass shootings
Texas school shooting
Missouri school shooting

Other pupils walked to safety, holding hands as they left their school surrounded by police cars, to a nearby church where they were reunited with their parents.

Officers with rifles, heavy vests and helmets could be seen walking through the school car park and around the perimeter of the building.

Helicopter footage also showed the officers looking around a wooded area between the campus and a nearby road.

Police said no officers were deployed to the school at the time of the shooting because it is a church-run school.

Nashville mayor John Cooper thanked emergency services for their response to the attack.

He tweeted: "In a tragic morning, Nashville 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."

'Unimaginable tragedy'

Democrat state representative Bob Freeman, whose district includes the Covenant School, called the shooting an "unimaginable tragedy".

"I live around the corner from Covenant and pass by it often. I have friends who attend both church and school there," Mr Freeman said.

"I have also visited the church in the past. It tears my heart apart to see this."

The Covenant School has about 200 students from pre-school to sixth grade and was founded as a ministry of Covenant Presbyterian Church in 2001, according to the school's website.