Two hours before the National Rifle Association told the country that guns were not to blame for the massacre at Sandy Hook Elementary School, U.S. Secretary of Education Arne Duncan today said that "reasonable people" should be able to overcome their differences on the issue and work to craft tougher laws.

Duncan, a member of Vice President Joe Biden's new task force charged with finding solutions to America's gun violence, said the goal should be to support "common sense" measures such as banning "assault weapons" and high-capacity ammunition, and closing gun-show loopholes in the background-check process.

"Reasonable people should be able to agree on these restrictions," Duncan said, speaking at an elementary school in Northeast Washington today. "As the president has pointed out, many of these ideas are backed by members of the NRA and were, in fact, supported by President Reagan."

NRA executive vice president Wayne LaPierre offered other ideas in his news conference today, including the addition of armed guards at every school.

White House Press Secretary Jay Carney said earlier this week that President Obama would support legislation that Democratic Sen. Dianne Feinstein of California intends to introduce, prohibiting the purchase and ownership of so-called assault weapons.

Duncan's speech served as the keynote at a panel on security challenges in D.C. schools, which began with a moment of silence for the victims of the Newtown shooting, during which the only sound in the Neval Thomas Elementary School auditorium was the clicking of camera shutters.

"I don't pretend to have all the answers but since last Friday a week ago, I do believe the world has fundamentally changed," Duncan said.

In addition to school administrators, Duncan said he wanted to talk with gun owners, hunters and sport shooters to get their advice on what leaders can do to secure schools.

"We have common values that go far beyond the constitutional right to bear arms," Duncan said. "We value the right to live our daily lives and to pursue our dreams without fear, but last week the dreams of 26 people in Newtown Connecticut were cut short at an elementary school because one disturbed man was mad at the world."

The Newtown shooting has also turned the spotlight on the weaknesses of mental health care in the United States, a subject Duncan briefly addressed.

"Are we doing enough to be sure information about mentally ill individuals who pose a violent threat is shared on schools and campuses?" Duncan asked.

Duncan questioned what shooter Adam Lanza, 20, might have done if he had not had access to the weapons his mother, Nancy, purchased legally.

"Maybe he would just be punching his pillow; his mother would still be here to give him support," Duncan said. "And there would still be 26 families in Newtown Connecticut who were preparing to celebrate the holidays instead of attending funerals.

"Unfortunately, it is too late for them," he added. "It is not too late for America."