Connecticut State Police lieutenant Paul Vance told reporters outside the school that the "shooter was deceased inside the building."
He said the shooting resulted in "several fatalities including students and staff."
The police has recovered a 9mm handgun from the scene. Officials said the shooter wore black combat dear and a military vest.
There was also some confusion initially about the number of shooters as some reports suggested two men were likely involved in the shooting episode.
Fox News quoted a law enforcement official as saying that the 20-year-old shooter is believed to be a father of one of the students at the school.
Image: Parents leave a staging area after being reunited with their children following a shooting at the Sandy Hook Elementary School in Newtown, Conn., about 60 miles (96 kilometers) northeast of New York City, Friday, Dec. 14, 2012. An official with knowledge of Friday's shooting said 27 people were dead, including 18 children. It was the worst school shooting in the country's history. (AP Photo/Jessica Hill)