Mark Kelly, the husband of former Rep. Gabrielle Giffords (R-Ariz.), struck a confident note Sunday that Congress would be able to advance new gun-control measures in 2013.

Appearing on "Fox News Sunday," Kelly contended that efforts to achieve universal background checks for purchasing guns, and closing the gun-show loophole were issues Congress could address in a bipartisan fashion, while acknowledging it will be difficult.

"In the United States of America, we solve difficult problems," he said. "We can fix this."

"I think that's very possible to get that done. Gabby and I are going to work as hard as we can to do whatever we can to get common sense solutions," he added.

Kelly reiterated his support for Americans to own guns, and noted that both he and Giffords were gun-owners. But he argued tougher restrictions on the ability to purchase guns, particularly by criminals and the mentally ill, are needed to protect the public.

"I don't think you'll find a person who is a stronger defender of the Second Amendment than me," he said "But this isn't about the Second Amendment anymore, this is about public safety."

Kelly, who has formed a group with Giffords to push for improved gun control, also argued in favor of a ban on high-capacity magazines, including the type used by Jared Loughner in the Arizona shooting that wounded Giffords and killed others.

Kelly contended that if Loughner could only use magazines that held fewer rounds than the kind he used, which held 33, lives would have been saved in that shooting.

"You would have had a lot less people shot, a lot less people murdered," he said.

Among those who may have been saved by limits on magazine size was nine-year old Christina Taylor Green, the youngest victim of the Tucson shooting, Kelly said. He said that she was shot with a bullet that would not have existed in a smaller magazine.

"She likely would be alive today, because she was shot with a bullet after round number 13," he said.

While pursuing new restrictions, Kelly also pushed for the government to enforce the laws already on the books. In particular, he said the government should be more active in pursuing charges against people who fail a criminal background check in an attempt to buy a gun.