All fatalities and injuries took place inside one classroom at Robb Elementary School in Uvalde, Texas, according to Lt. Chris Olivarez, spokesperson for the Texas Department for Public Safety.
The shooter barricaded himself in one room, killing two teachers and 19 children, he said.
"Just goes to show you the complete evil from this shooter," Olivarez told CNN's John Berman and Shimon Prokupecz.
As the shooting was taking place, officers were going around the school, breaking windows and trying to evacuate children and staff. They were then able to force entry into the classroom where the shooter was, he said.
All the victims have been removed, identified and their families have been notified, the lieutenant said. Multiple children were wounded inside the classroom, according to Olivarez, but there is no exact number as to how many at this time.
"It's a small classroom, you can have anywhere from 25 to 30 students in there, plus there were two teachers in there. ... So don't have exact number of how many students were in that classroom, but it could vary ... It was a classroom setting, a typical classroom setting where you have mass groups of children inside that classroom all together, with nowhere to go," Olivarez said.
Olivarez said there was no chase with law enforcement before the shooter crashed a car near the school.
When asked if the school was a target, Olivarez said there are still "a lot of unanswered questions."
"We're trying to determine that, that's why we're working with FBI right now to kind of look back to see if there were any indicators, any red flags, looking at social media. What we know about the shooter is that he is a resident here in Uvalde, he did attend one of the local high schools, he lived with his grandparents, was unemployed, no friends, no girlfriend that we can identify at this time, no criminal history, no gang affiliation as well," he said.
Olivarez said the shooter had one rifle in his possession when he went into the school, and authorities are working to determine what type of rifle and the capacity.
The shooter was wearing "a tactical vest carrier with no ballistic panels; so typically those type of carriers are used by tactical teams, SWAT teams, where they can place magazines, extra ammunition inside those carriers and be able to move in a tactical formation," Olivarez said.
Olivarez said his grandmother — whom the shooter shot beforehand — is still alive and authorities are trying to locate his grandfather and immediate family members.
CNN's Raja Razek contributed reporting to this post.