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A heavily armed former student killed three young children and three staff in what appeared to be a carefully planned attack at a private elementary school in Nashville on Monday, before being shot dead by police.

Chief of Police John Drake named the suspect as Audrey Hale, 28, who left behind a manifesto and had maps of the school detailing surveillance and entry-exit points.

The suspect was "prepared for a confrontation with law enforcement," the police chief told reporters following the latest outburst of gun violence in the United States.

In an interview with NBC News, Drake said the suspect was likely plotting a broader attack, as the manifesto "indicates that there was going to be shootings at multiple locations, and the school was one of them."

Armed with at least two assault rifles and a handgun, Hale entered The Covenant School, a Christian academy, from a side entrance, allegedly shooting through a door - firing multiple shots while advancing through the building, according to police.

Police identified the six victims, saying one of the three children was eight years old and two were aged nine, while the adults killed were aged 60 to 61.

One of the victims, Katherine Koonce, is listed as head of the school on the academy's website.

There was some initial confusion about the shooter's gender identity, but police later said Hale was transgender.

Officers were on the scene within about 15 minutes of receiving the first emergency call at around 10 am (1500 GMT), engaging the shooter, who returned fire before being shot dead, police said.

Television images showed children holding hands as they left the school. One photograph showed a child sobbing through the window of her yellow school bus as it pulled away from the crime scene.

Avery Myrick said her mother, a pre-kindergarten teacher at Covenant, hid as shots rang out through the school.

I call on Congress again to pass my assault weapons ban.

It's about time we make some more progress.

— President Biden (@POTUS)

"She said she was hiding in the closet, and that there was shooting all over and that they had potentially tried to get into her room, and just that she loved us," Myrick told WSMV4 television, an NBC local affiliate.

On Monday night, as the country digested another mass shooting that claimed the lives of children, people left flowers and stuffed toys at a growing makeshift memorial outside the school. Some kneeled in prayer.

Stacie Wilford, a nurse, said it was "so scary" to have a shooting so close to home. She lives nearby and has an eight-year-old who attends a school only two miles down the road from The Covenant School.

"Whenever you hear about school shootings in other states, yes, you feel it, but when it's at your back door, it just sets in differently," Wilford told AFP.

School shootings are alarmingly common in the United States, where the proliferation of firearms has soared in recent years.

President Joe Biden described the latest shooting as "sick" and said gun violence was "ripping the soul of this nation," as he urged Congress to pass a ban on the assault weapons often used in mass shootings.

The Covenant School is a private Presbyterian institution with just over 200 students, from preschool to roughly age 12.

The school was founded by and housed in the Covenant Presbyterian Church, part of a theologically conservative denomination, The New York Times reported.

The Times said one of the children who died in the shooting was Hallie Scruggs, the daughter of the church's pastor, Chad Scruggs.

Police chief Drake said investigators were working on a possible motive but that it was "not confirmed."

Asked whether Hale's gender identity may have been a factor, Drake said: "There is some theory to that, we're investigating all the leads."

There have been 129 mass shootings - defined as incidents in which four or more people were shot or killed - so far this year, according to data from the Gun Violence Archive.

Biden's calls for Congress to reinstate the national ban on assault rifles, which existed from 1994 to 2004, have 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 deadlock in Washington has come 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.

The 2018 murder of 14 students and three staff members in Parkland, Florida fueled a nationwide movement, led by young people, to demand stricter gun controls - but failed to spur significant action in Congress.