Lt Paul Vance said the gunman was also dead, but did not identify him.
However, officials told US media the killer at Sandy Hook Elementary School, Newtown, was a 20-year-old son of a teacher at the school.
Newtown is now one of the worst school shootings in US history, after 32 died at Virginia Tech in 2007.
Early reports named 24-year-old Ryan Lanza as the gunman, but anonymous officials later said his brother Adam, 20, was the suspect.
Ryan Lanza was being questioned by police, the Associated Press and New York Times reported.
Lt Vance said 18 children were pronounced dead at the school, and two died after they were taken to hospital. Six adults were also killed. The gunman died at the scene.
One person was also injured, and police were investigating a "secondary" crime scene in Newtown, where another victim was found dead, Lt Vance said.
Dressed in black and wearing a bullet-proof vest, the gunman is thought to have had several weapons at the school, although it is not clear whether he used more than one.
The attack took place in two rooms within a single section of the school, police have said.
Night has fallen in Newtown, and school officials announced that a memorial service would take place at 19:00 EST (00:00 GMT).
'Innocence torn away'
Friday's shooting is the third major gun attack in the US in 2012.
In July an attacker killed 12 people at a premiere of a Batman film in Aurora, Colorado. In August six people died at a Sikh temple in Wisconsin.
Just this week two people died in a shooting at a shopping mall in the state of Oregon.
At the White House, an emotional President Barack Obama cited those incidents as he called for "meaningful action... regardless of politics".
"Our hearts are broken today, for the parents, grandparents, sisters and brothers of these children, and for the families of the adults who were lost."
Mr Obama offered condolences to the families of survivors too, saying "their children's innocence has been torn away from them too early, and there are no words that will ease their pain".
He wiped tears from his eyes as he spoke of the "overwhelming grief" at the loss of life.
Connecticut Governor Dannel Malloy called the attack a "tragedy of unspeakable terms", saying "you can never be prepared" for an event like this.
He spoke after spending the day visiting the victims' families.
The American flags on Capitol Hill in Washington DC have been lowered to half-mast in the wake of the attack.
Schools locked down
Police arrived at the school soon after 09:40 local time (14:40 GMT), answering reports that a gunman was in the school's main office and one person had "numerous gunshot wounds".
One witness speaking to CNN said that shots were heard coming from the hall. There "must have been 100 rounds" fired, she told the channel.
Local media have reported that firefighters instructed children to close their eyes and run past the school's office as they exited the building.
Scores of officers at the scene carried out a full search of the site. Classes were cancelled as the situation developed.
Sandy Hook School - described by correspondents as a highly rated school has more than 600 students in classes from Kindergarten to 4th Grade - spanning the ages five to 10.
Schools across the district were immediately on lock-down as a preventive measure, officials said.-British Broadcasting Corporation (December 14, 2012 22:24GMT)
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