The 28-year-old attacker, who came from the southern US city, was killed by police after a confrontation with officers following the assault at the Covenant School.

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

She has not yet been publicly identified.

Officers started receiving reports of an attack at 10.13am (4.13pm UK time) on Monday 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) - the whole tragedy lasted around 14 minutes.

They are investigating a possible link between the attacker and the school, which teaches pupils 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.

So far this year, there have been 89 US school shootings - defined as anytime 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.

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 Congress to pass his assault weapons ban.

Read more: US mass shootings

No one else was shot in the latest assault.

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

Nashville mayor John Cooper has 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.