The perpetrator was killed by police after a confrontation with officers following the assault at the Covenant School.

Police said the suspect, who appeared to be in her teens, was armed with two assault-type rifles and a pistol.

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

Two officers from a five-member team shot at the suspect in a reception area and she was dead by 10.27am (4.27pm).

John Howser, from Vanderbilt University Medical Center, earlier confirmed "three paediatric patients were transported to Monroe Carell Jr Children's Hospital at Vanderbilt, all having suffered gunshot wounds".

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

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

It was not clear whether anyone else was wounded in the attack.

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.

The Nashville Fire Department said on Twitter there were "multiple patients".

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

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

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."

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.