Malloy suggested Connecticut officials and residents have a responsibility to the 20 children and six staffers gunned down at Sandy Hook Elementary School. He promised action on gun control and on providing treatment for the mentally ill.
The governor also challenged the National Rifle Association, which has proposed placing armed guards or police officers in every school.
"And when it comes to preventing future acts of violence in our schools, let me say this: More guns are not the answer. Freedom is not a handgun on the hip of every teacher, and security should not mean a guard posted outside every classroom," Malloy said. "That is not who we are in Connecticut, and it is not who we will allow ourselves to become."
Two Newtown officials, First Selectwoman Patricia Llodra and School Superintendent Janet Robinson, sat with Malloy's wife, Cathy, as he delivered the speech.
Republican legislators said afterwards they are sure they can work with the majority Democrats for bipartisan gun control and mental health legislation.
With his focus on the Newtown shootings, Malloy spent less time talking about the Connecticut budget. But he defended a tax increase he said helped Connecticut balance its budget two years ago.
"We cut more than we added in new revenue," he said. "And even after revenues came in short -- as they did in 31 other states -- we know today that our budget as enacted fixed more than 90 percent of the problem. Last month, Democrats and Republicans came together to make sure we closed that final gap without raising taxes."