NEWTOWN, Conn. — Parents of children slain in the Connecticut school massacre held photos of their sons and daughters, cried, hugged and spoke in quavering voices as they called for a national dialogue to help prevent similar tragedies.

“I do not want to be someone sharing my experience and consoling another parent next time. I do not want there to be a next time,” said Nicole Hockley, whose son Dylan was among the 20 first-graders and six adults killed by a gunman a month ago at Sandy Hook Elementary School.

Members of the newly formed group Sandy Hook Promise spoke out as politicians from Maine to New Mexico marked the one month that has passed since the shooting with renewed demands for tighter gun control.

The Sandy Hook group says it wants to have open-minded discussions about a range of issues, including guns, mental health and safety in schools and other public places. Several speakers said they did not believe there was a single solution.

“We want the Sandy Hook school shootings to be recalled as the turning point where we brought our community and communities across the nation together and set a real course for change,” said group co-founder Tom Bittman.

While the Sandy Hook group did not offer specific remedies, mayors and governors in favor of tighter gun restrictions lobbied for a series of them Monday.

New York Mayor Michael Bloomberg addressed a summit on gun violence at Johns Hopkins University in Baltimore and argued for greater federal gun control, including background checks for all purchases and a federal crackdown on trafficking.

“Every state in the union has citizens killed by guns coming from another state and every state is powerless to stop the mayhem,” Bloomberg said.

Bloomberg is co-chairman of Mayors Against Illegal Guns, whose members spoke out Monday in cities including Portland, Maine; Fort Wayne, Ind.; and Santa Fe, N.M.

Chicago Mayor Rahm Emanuel said he has ordered an analysis of city employee pension funds to see if they hold companies that make or sell assault weapons. In Cranford, N.J., a group of mayors backing new restrictions were joined by a man whose 23-year-old son was shot to death in the 2007 massacre at Virginia Tech.

“I’m just one member of a Virginia Tech family, Newtown has theirs, Aurora has theirs, Tucson has theirs, and now we’re starting to come together,” Michael Pohle said. “This coalition is growing, and it’s going to become more powerful, and we’re going to have the ability to influence elections as well.”

The gun control debate heated up after 20-year-old Adam Lanza shot his way into Sandy Hook Elementary School on Dec. 14 and killed 26 people before committing suicide as police arrived. He also killed his mother at their Newtown home before driving to the school and carrying out the massacre.

President Barack Obama is reviewing proposals from Vice President Joe Biden, who is leading a task force on ways to reduce gun violence. Obama told reporters Monday he is looking at actions he can take on his own to confront gun violence amid resistance from the National Rifle Association and wariness among lawmakers from both parties.

The NRA has fiercely opposed new gun control laws and has called for “a meaningful conversation” about school safety, mental health issues and marketing violence to children.

A number of governors were already moving ahead with proposals to toughen state laws.

New York’s Legislature was expected to vote as early as Monday night on a measure to tighten gun laws in a state that already has among the nation’s strictest gun rules. The tentative deal would further restrict New York’s ban on assault weapons and limit the size of magazines to seven bullets, rather than the current 10. It also would also make it easier to secure civil confinement for people determined to be a threat.

In Delaware, Gov. Jack Markell on Monday proposed background checks for private gun sales and a ban on military-style weapons. A package of gun control proposals also included a ban on magazines holding more than five rounds for rifles and 10 rounds for handguns, and a ban on guns within 1,000 feet of schools.

Maryland Gov. Martin O’Malley, speaking at the same Baltimore summit as Bloomberg, said he will be advocating a broad array of proposals this legislative session, including a ban on military-style weapons, stricter licensing requirements, school safety and mental health concerns.

“This will be a comprehensive legislative package to prevent gun violence, and it addresses not only the guns but also mental health and school safety,” O’Malley said.

Jeremy Richman, whose daughter Avielle was killed at Sandy Hook, said a deeper understanding of mental health issues is essential. He and his wife, Jennifer Hensel, started a foundation to explore issues such as risk factors and successful interventions.

Richman spoke at the same news conference as Hockley, who said she still finds herself reaching for her son Dylan’s hand or expecting him to crawl into bed with her for a hug before school.

“It’s so hard to believe he’s gone,” she said.