Sen. Roy BluntRoy Dean BluntGOP senator: Capitol Hill's sexual harassment reporting protocol is 'totally inappropriate' Senate passes resolution requiring mandatory sexual harassment training Strange bedfellows on criminal justice reform could offer Trump a legislative win MORE (R-Mo.) on Sunday said he's willing to explore measures to prevent future tragedies like the mass shooting at Sandy Hook Elementary School last month, but cautioned that past firearm bans had made little difference.

"Let's do things that will make a difference here rather than take one more opportunity to go on an old agenda," Blunt said on Fox News Sunday. "We had bans on things for a decade that didn't seem to make any difference at all.”

Blunt noted that the shooter at Sandy Hook, Adam Lanza, had a history of mental problems. He said Congress should look at how officials can improve the sharing of mental-health data so severely mentally ill people cannot purchase firearms. But he also warned that any proposals aimed at reducing gun violence should not conflict with the Second Amendment.

"You've got to have proposal that works that doesn't create a problem of people not able to have the firearms that they'd like to have," Blunt said. "The Second Amendment is there, It's part of the Constitution and you can't just decide you want to avoid the Constitution because you've come up with some reason that the Constitution no longer works. You have to come up with a real proposal and propose it to the Congress."

President Obama is calling on Congress to institute bans on assault weapons and high-capacity ammunition. But many GOP lawmakers say further gun-ownership restrictions will do little to stem the tide of gun violence.

Blunt has an "A" rating from the National Rifle Association. When President Obama unveiled his gun control plan this week, Blunt accused the president of "attempting to restrict the Second Amendment rights of law-abiding Americans."

Despite the upcoming battle in Congress over Obama's gun control proposals, Blunt said there was a chance this year for lawmakers to take steps to prevent future mass shootings.

"This is a moment [where] we can do something about mental-health information sharing, maybe about background checks and other things as well," he said.

Blunt, a member of the Senate Armed Services Committee, also said former Sen. Chuck HagelCharles (Chuck) Timothy HagelPentagon documents hundreds of serious misconduct cases against top brass Obama defense sec: Trump's treatment of Gold Star families 'sickens' me The Hill's 12:30 Report MORE (R-Neb.) "has got some questions to answer" during his confirmation process for Secretary of Defense. Blunt said he plans to meet with Hagel this week. 

"I think Chuck Hagel has got some questions to answer. One of those questions is going to be, why is it that the positions you held in the past about Iranian sanctions, about our support for Israel no longer appear to be your positions?" he said.

This story was updated at 11:47 a.m.