NEWTOWN, CONN. - Nelba Marquez-Greene put her two children on the school bus on the morning of Dec. 14. Only one came home.

Nicole Hockley still finds herself reaching for her son's hand in parking lots. "It's so hard to believe he's gone," she said.

The grieving parents and family members of those killed in the Sandy Hook Elementary School massacre gathered at a news conference Monday to help begin a campaign aimed at preventing the kind of bloodshed that has turned this quiet New England community into a national symbol of grief.

In some of their first public statements since the shooting that killed 20 children and six staff members at the school, the families of 11 of the children and adult victims called for a national dialogue on issues of mental health, school safety and what their nonprofit organization, called Sandy Hook Promise, described as "gun responsibility."

The gathering came as President Obama prepared to unveil gun-control proposals this week that are expected to call for a ban on the kind of assault weapon and high-capacity ammunition magazines used in the Newtown shooting.

But perhaps foreshadowing the difficult debates to come in Washington, group members declined to offer support for any specific measures, saying they needed time to educate themselves on the issues and emphasizing that the debate must be broader than gun control.

"It's only been 30 days, and for the past 30 days we've really been looking inward and supporting our community," said Tim Makris, a founder of the group whose fourth-grade son was not hurt. "We love the focus of the president, and we love that the vice president reached out recently to talk directly to the families that chose to meet with him."

Tom Bittman, another founder who had three children attend the school, said that many of the group members were gun owners. "We hunt; we target shoot," he said. "We protect our homes. We're collectors. We teach our sons and daughters how to use guns safely. We're not afraid of a national conversation in our community and in Congress about responsibility and accountability."

The news conference, which included other members of the community, was the first time a group of families has spoken publicly about the tragedy.

The families filed on stage, inside the Edmond Town Hall, holding hands and wearing ribbons of green and white, the school's colors. Some held photographs of their children. Some wiped away tears, still gripped in mourning.

"I hope that no parent, grandparent or caregiver of children ever has to go through that pain," said Marquez-Greene, whose 6-year-old daughter, Ana, died that day.

Ana's father, Jimmy Greene, sat clutching a large photograph of his smiling daughter.

Jeremy Richman and Jennifer Hensel, the parents of Avielle Richman, 6, who was killed, said they had started a foundation in her name to focus on research to identify "risk factors and measure success of mental health interventions."

"Like everyone here, we want to bring about changes that will stop a tragedy such as this from happening to any community again," said Richman, as he choked back tears.

David and Francine Wheeler, whose son Benjamin, 6, was killed, explained why they joined the campaign."What I have recently come to realize is that I am not done being the best parent I can be for Ben," David Wheeler said. "Not by a very long measure."

He added, "I would respectfully request that any parent that hears these words simply pause for a moment and think, ask yourself, what is it worth doing to keep your children safe?"

While it was clear they were still grasping for answers, they have joined a sad fraternity of people who have lost loved ones in such tragedies.

Hockley's son Dylan, 6, was found dead cradled in the arms of his favorite school aide, Anne Marie Murphy, who died apparently trying to shield him. Hockley said that since the shooting, she had felt "honored" to meet with the families of victims of past mass shootings. But, she added, she did not want to be someone consoling parents the next time such a shooting occurs.

"I do not want there to be a next time," she said.

The Associated Press contributed to this report.