A woman has opened fire at an elementary school in Nashville in the southern US state of Tennessee, killing six people, including three children.

The 28-year-old woman armed with two rifles and a handgun attacked the school on Monday morning.

The suspect is reportedly a local resident and a former student of the school.

Police shot the woman dead on the scene, and are investigating her motive.

The school is located in a residential area about 9 kilometers south of central Nashville.

Police say the school has about 200 students from preschool through sixth grade.

President Joe Biden said during an event at the White House that gun violence is ripping communities apart, ripping at the very soul of the nation.

He stressed, "We have to do more to protect our schools."