Chris and Lynn McDonnell, whose daughter Grace was among 20 first graders and six educators killed in December, spoke Thursday at a gun violence conference in Danbury.
"We ask our representatives to look into their hearts and remember the 26 beautiful lives we lost and pass meaningful laws to help prevent this from happening again," Lynn McDonnell said, sparking a standing ovation.
Chris McDonnell said he hoped the moral responsibility of gun owners would be discussed.
Vice President Joe Biden was scheduled to speak later Thursday at the conference a few miles from the scene of last year's Newtown school shootings.
The conference at Western Connecticut State University is to push President Barack Obama's gun control proposals. It was organized by members of the state's congressional delegation.
Connecticut Gov. Dannel P. Malloy revealed his own gun control package ahead of his appearance at the conference. He said Thursday that he wants to immediately ban high-capacity ammunition magazines, require background checks for the transfer of any firearm and expand the state's assault weapons ban. The Democrat has expressed frustration with the pace of the state legislature's efforts to form a response to the Newtown tragedy.
The gunman, 20-year-old Adam Lanza, killed his mother at their Newtown home before going to the school and slaughtering 20 children and six adults. He committed suicide as police arrived.
As a teenager, Lanza studied at Western Connecticut State, earning a 3.26 grade point average before taking his last class in the summer of 2009. Classmates remembered him as quiet, a trait some thought was a result of him being younger than his peers.
Obama is pushing for universal background checks for gun owners, a ban on many military-style weapons and a limit on the size of magazines.
U.S. Sen. Richard Blumenthal, who organized the conference with two other members of the state's congressional delegation, said those measures are achievable. He said the Newtown shooting dramatically changed the prospects for gun control.
"Two months ago gun violence and measures to stop it were untouchable," Blumenthal said. "The forces of resistance as strong as they once appeared are a shadow of what they were."
A second panel was to discuss mental health and school safety initiatives.
Malloy, Newtown First Selectman Pat Llodra, state police Capt. Dale Hourigan and the mayors of Bridgeport and Hartford planned to participate, along with other experts in the fields of mental health, law enforcement and education.
Gun makers and lobbyists weren't invited to participate in the conference, but Blumenthal said gun rights advocates will have opportunities in hearings and other forums to express their points of view.