CNN previously reported that the shooter entered the Covenant School through a side door and was armed with at least two assault-style rifles and a handgun.
The assailant -- who police said was believed to be a former student at the school -- fired multiple shots as she advanced through the building.
Officers were on the scene within about 15 minutes of receiving the first emergency call around 10:00 am (1500 GMT), engaging the shooter who returned fire before she was shot dead, Aaron said.
School shootings are alarmingly common in the United States, where the proliferation of firearms has soared in recent years, though female shooters are extremely rare.
There was no initial indication of a motive for the Nashville attack.
President Joe Biden described the latest shooting as "sick" and said gun violence was tearing the nation's "soul," as he urged Congress to pass a ban on the assault weapons commonly used in mass shootings.
"It's ripping our communities apart, ripping the soul of this nation, ripping at the very soul of the nation," he said.
Police spokesman Aaron said officials were still working to identify the three students and three adults killed in the attack, as well as the shooter.
He said there were no other injuries.
"All of the remaining students were able to be escorted out of the building with faculty and staff," Kendra Loney of the Nashville fire department said.
"But we are sure that they heard the chaos that was surrounding this, so we do have mental health specialists and professionals that are at that reunification site for both the students and the families."
The Covenant School is a private Presbyterian institution with a little more than 200 students in preschool to roughly age 12. The adult victims were among 40 to 50 staff at the school.
At the White House, Press Secretary Karine Jean-Pierre asked what Republicans were waiting for to "step up and act to pass the assault weapons ban."
Biden's calls for Congress to reinstate the national ban on assault rifles, which existed from 1994 to 2004, has run up against opposition from Republicans, who are staunch defenders of the constitutional right to bear arms and have had a narrow majority in the House of Representatives since January.
The legislation deadlock in Washington has come despite public uproar over high-profile massacres such as the one at Sandy Hook elementary school in Connecticut in 2012, when 26 people, including 20 children were killed.
Last year, a shooter in Uvalde, Texas, killed 19 students and two teachers.
Between those two tragedies, the shooting of 14 students and three staff members in Parkland, Florida in 2018 fueled a nationwide movement, led by young people, to demand stricter gun controls.
But despite huge demonstrations, Congress has not adopted significant new legislation, with many lawmakers backed by the influential National Rifle Association (NRA).
Several elected officials in the state of Tennessee on Monday took to social media to express their shock over the latest outburst of gun violence to shock the country.
"Devastated and heartbroken about the tragic news at Covenant School," tweeted Senator Bill Hagerty.
With additional reporting by AFP