Eighteen youngsters were pronounced dead at the scene and two others died later at the hospital, state police Lt. Paul Vance told a press conference.
The six adult victims at the school included the principal of Sandy Hook Elementary, while another adult found slain at a different location is thought to have been killed by the same shooter.
The perpetrator apparently took his own life.
"We are not going to confirm the identity of the shooter," Vance said, adding that police could not release additional details pending completion of the investigation.
He revealed, however, that one person who was shot inside the school survived and said an FBI team had already arrived in Newtown to assist in the probe.
All of the shootings at Sandy Hook took place in two classrooms, Vance said.
"Earlier today, beautiful children had their lives taken away from them," Connecticut Gov. Dannel Malloy said at the same press conference.
"You can never be prepared for this type of tragedy," he said.
"We have endured too many tragedies in recent years," an emotional President Barack Obama told reporters at the White House. "Our hearts are broken today."
The president ordered flags at government buildings flown at half-staff in honor of the victims and the White House announced that because of the massacre, Obama would not be making a visit to Portland, Maine, scheduled for next Wednesday.
Authorities received a 911 call at 9:41 a.m. Friday and Connecticut state police quickly dispatched emergency units to the school in Newtown, which has 450 students. EFE