The shooter, identified by police as Natalie Rupnow, who also went by Samantha, was a student at the Abundant Life Christian School in Madison, Wisconsin, the state capital.
In one key way, the Madison attack is an outlier among US school and mass shootings: Women and girls are far less likely to carry them out than male attackers. Only about 3% of all US mass shootings are perpetrated by females, studies show.
"Identifying a motive is our top priority, but at this time it appears that the motive was a combination of factors," Madison Police Chief Shon Barnes told a news conference.
Barnes did not provide more detail, saying he didn't want to jeopardise the investigation.
Investigators are examining the girl's cell phone, computer and online posts as well as looking into verifying a possible manifesto that the shooter may have left behind.
Some details of Rupnow's life have begun to emerge.
Police have confirmed the name of the street where she lived in Madison. Online records show a person named Jeffrey Rupnow lives on the same street, and a Facebook profile belonging to a Jeff Rupnow in Madison shows photos of a newborn daughter named Natalie Lynn from 2009, 15 years ago.
Jeff Rupnow's cover photo, posted in August, shows what appears to be a teenaged girl trap shooting with a shotgun at a local club. In a comment on the site, Jeff Rupnow says he and his child joined the club in the spring and "have been loving all every second of it."
Rupnow could not be reached for comment.
In the photo, the girl is wearing a T-shirt of the German band KMFDM. The teenaged shooters in the 1999 Columbine school massacre in Colorado were known to be avid fans of the band, and one of the killers posted the band's lyrics on his website.
At the time, KMFDM issued a statement condemning the Columbine attack, expressing sympathy for the victims and affirming its music was intended to stand against violence.
A RARE OCCURRENCE
The sheer number of school shootings since Columbine make it almost inevitable that some will be carried out by female students, experts said. But it remains a rarity.
"Historically, there are factors that have led men to commit these shootings," said Jonathan Metzl, a sociology and psychiatry professor at Vanderbilt University and an expert on gun violence.
Males often have easier access to firearms, and many shooters model themselves after previous attackers, most of whom were men. Some sociologists also view mass shootings as "reflective of a pathology of toxic masculinity," Metzl said. And, of course, men are more likely to commit violent crimes in general, not just school shootings.
But other factors common to school shootings - bullying, isolation, social media - are not specific to boys. Data also shows an increase in aggression and violence among adolescent girls in recent years, according to Elizabeth Dowdell, a professor of nursing at Villanova University who has studied school shootings.
Monday's shooting took place in a study hall classroom of the small, private school just before 11am. Two students remained in critical condition on Tuesday, while several other victims suffered less serious injuries, officials said.
Police said Rupnow used a pistol, but have not said how it was obtained. Earlier this year, the Michigan parents of a school shooter in that state were found guilty for their role in allowing their son to have access to the gun he used to kill.
Wisconsin officials said at Tuesday's media conference that it was far too early to say if Rupnow's parents could be held legally responsible. Police Chief Barnes said that for now it appeared that such charges were not warranted.
School shootings have become a near-daily occurrence in the United States, with 322 of them this year, according to the K-12 School Shooting Database. That is the second highest total of any year since 1966 - topped only by last year's total of 349.
Polling shows American voters favour stronger background checks on gun buyers, temporary limits on people in crisis and more safety requirements for gun storage at homes with children. Yet political leaders have largely declined to act, citing the US constitutional protection for gun owners.
Dane County Executive Melissa Agard said at Tuesday's news conference she wanted to see stricter gun laws in Wisconsin - including "Red Flag" laws that could result in guns being confiscated from at-risk people and also laws requiring the safe storage of guns in homes.
"Let us remember this fact: gun violence is the No 1 killer of children in this country," Agard said. "That's a legacy we cannot accept."
