US investigators say a fatal school shooting in the southern state of Tennessee that claimed the lives of six people was premeditated.

A 28-year-old local resident opened fire Monday morning at an elementary school in Nashville, killing three children and three adults before being shot dead by police.

The shooting took place at a private Christian school in a residential area about 9 kilometers south of central Nashville. The Covenant School has about 200 students from preschool through sixth grade.

Police say the shooter, who was armed with two AR-15 assault rifles and a handgun, was a former student of the school.

They also say the shooter claimed to be transgender.

Investigators found detailed maps of the school and a manifesto when they searched the shooter's home.

Commenting on the tragedy, President Joe Biden said, "We have to do more to stop gun violence." He added, "We have to do more to protect our schools."