Following a search of the suspect's home, who was killed by police during the attack, police believe it was carefully and in detail.
"We have some documents that we're going through that relate to this day, the actual event," John Drake tells reporters.
"We have a map drawn out of how all this would happen.
Motive not clarified
When the first police patrols arrived at the Christian private school in Nashville on Monday morning local time, several shots were heard from the second floor.
The officers walked up the stairs and encountered the gunman, who was armed with at least three firearms. There was a shooting and the 28-year-old was shot dead, Nashville police said during a press briefing after the attack.
No motive for the murders is known, but according to police, the shooter is believed to have previously been a student at the school.
Biden: It's terrible
The children who were killed were aged nine. The three adults killed were in their 60s and employees of the school, according to police.
About 200 students attend the school, which accepts children from preschool age up to the age of twelve.
"It's terrible, a family's worst nightmare," US President Joe Biden said of the school murders.
Biden also urged Congress to pass his ban on a particular type of semi-automatic weapon.
The White House and federal buildings in the U.S. will fly flags at half-mast through Friday, in response to the deadly attack.