The young shooting victims were pronounced dead after arrival at Monroe Carell Jr. Children’s Hospital, officials said.
All three students had gunshot wounds from the shooting at The Covenant School, a Presbyterian school for about 200 students aged 4 to 12.
Three adults were also later pronounced dead.
Young students were seen holding hands as they were escorted out of the school by police to a nearby church to be reunited with their parents.
Police officers with rifles, heavy vests and helmets could be seen surrounding the school car park and the grassy perimeter of the building on Monday morning.
The Covenant School was founded as a ministry of Covenant Presbyterian Church in 2001, according to the school’s website.
The school is located in Green Hill, just south of downtown Nashville and home to the famed Bluebird Café – a beloved spot for musicians and songwriters.
The White House spokeswoman, Karine Jean-Pierre, called the shooting “heartbreaking” and urged Republicans to back Mr Biden’s push for an assault weapons ban.
“How many more children have to be murdered before Republicans in Congress will step up and act?” she said during a press briefing Monday. “We need to do something.”