Dannel P Malloy gathered with other officials on the steps of the town hall as the bell rang 26 times in memory of each life lost at Sandy Hook Elementary School.
The gunman also killed his mother before the massacre, and himself afterward.
Officials didn’t plan any formal remarks on Friday morning, when similar commemorations were planned throughout the country.
The White House said US President Barack Obama would privately observe the moment of silence.
Governors across the country also called for a moment of silence at 9:30 am (local time).
New Jersey Governor Chris Christie signed an executive order for a statewide moment of silence for the victims of the shooting.
Christie wanted the citizens of New Jersey to reflect on the 20 children and six educators killed at Sandy Hook Elementary School one week ago.
Christie said Americans owe it to the children killed to have a thoughtful conversation about gun control, mental illness and other issues.
NRA calls for armed police officer in every school
The nation’s largest gun-rights lobby is calling for armed police officers to be posted in every American school to stop the next killer “waiting in the wings.” The group’s top lobbyist, Wayne LaPierre, during a conference, said, "The only thing that stops a bad guy with a gun is a good guy with a gun.”
Photos: Shah Rukh Khan, Shweta Bachchan at Karan Johar's book launch
Photos: Sunny Deol with sons Karan and Rajvir at Mumbai airport
Photos: 10 beautiful moments that capture winter around the world
Photos: Karisma Kapoor, Preity Zinta, Shraddha Kapoor at Mumbai airport
Spotted: Anushka Sharma and Diljit Dosanjh at Mumbai studio