Slain Nashville school shooting suspect was a 28-year-old woman: police
Officers responding to a shooting at Covenant School, Covenant Presbyterian Church, in Nashville, Tennessee. (Handout)

A 28-year-old woman killed three children and three staff at a private elementary school in Nashville, Tennessee, on Monday before being shot dead by police, in the latest outburst of gun violence to shock the United States.

Armed with at least two assault rifles and a handgun, the shooter entered the Christian Covenant School from a side door before opening fire, Nashville police spokesman Don Aaron told a press conference.

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.

The young woman, identified by police as a 28-year-old from Nashville, fired multiple shots as she advanced through the school, Aaron said. There was no initial indication of a motive for the shooting.

"We now know that there are three students who were fatally wounded, as well as three adults inside the school," Aaron said, specifying that the adults were among the 40-50 staff at the school.

"We are working to identify those victims, including 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.

"We were on scene to help them mitigate anyone from seeing exactly what else was going on," she 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.

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.

The White House called the latest school shooting "heartbreaking" and urged Republicans to back President Joe Biden's push for a ban on assault weapons commonly used in US mass shootings.

Press Secretary Karine Jean-Pierre said Biden had been briefed on the "heartbreaking news of another shooting of innocents" and she asked what Republicans were waiting for to "step up and act to pass the assault weapons ban."

Several elected officials in the state of Tennessee likewise took to social media to express their shock.

"Devastated and heartbroken about the tragic news at Covenant School," tweeted Senator Bill Hagerty.

"I'm grateful to law enforcement and first responders for their heroic actions."

Senator Marsha Blackburn thanked first responders and offered "prayer for those affected."

Legislation tackling gun violence has met with deadlock in Washington despite the 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.