Kelly's wife, former U.S. Rep. Gabrielle Giffords, D-Ariz., was the target of multiple death threats after voting for healthcare reform in the House. She was seriously wounded Jan. 8, 2011, at a public event outside a supermarket near Tucson when a gunman shot her in the head, killed six others including a federal judge and a child, and wounded 13. She resigned her congressional seat last year to concentrate on her recovery.
In an appearance on Fox News "Sunday," Kelly said Jared Loughner, the shooter, had been expelled from Pima Community College because of his mental illness.
"If his condition was entered into the system, into the criminal background check system, and he went to do that background check, I would assume that he would have been rejected [for a weapon]," Kelly said. "So, in the case of Jared Loughner, if Arizona would have entered 121,000 records that they had not entered into the system, if his record was one of those ... he probably would have been rejected."
In addition to making sure states enter mental illness information and require universal background checks, Kelly said he'd like to see legislation passed to prevent guns from holding too many rounds. He said if the gun Loughner used during his wife's shooting held 10 rounds instead of 33, it would have made a difference.
"As he tried to reload one 33-round magazine for another 33 round magazine, he dropped the magazine, and that gave time for a woman named Patricia Maisch to grab it and it gave time for a couple of people to restrain him," Kelly said.
"If, let's say, for a second, that that was a 10-round magazine and the same thing happened, you would have had a lot less people shot and a lot less people murdered."
Loughner is serving life in prison without parole.