"If it's crazy to call for putting police and armed security in our schools to protect our children, then call me crazy," NRA CEO Wayne LaPierre said of the anger following his initial news conference.
NRA President David Keene later told CNN the group supports schools choosing whether they want armed guards.
Kelly: 'Good guys with guns' aren't the whole answer
LaPierre made clear his group believes that more guns, not fewer, are necessary for security.
"The only thing that stops a bad guy with a gun is a good guy with a gun," he said.
Kelly said he knows from personal experience that that's not the case.
The day Jared Loughner shot Giffords and 18 other people at a public event in Tucson, there was such a "good guy," Kelly argued in an interview with ABC.
A man came out "of the store next door and nearly shot the man who took down Jared Loughner," Kelly said. "The one who eventually wrestled (Loughner) to the ground was almost killed himself by a good guy with a gun, so I don't really buy that argument."
Giffords and Kelly want to require comprehensive background checks for private sales of firearms, ABC reported. And Kelly said he does not believe an extended magazine is needed for those who have guns for sport.
Gunmen have used high-capacity weapons in numerous shootings, including one at a movie theater in Aurora, Colorado, and Newtown, where gunman Adam Lanza had four weapons.
Sen. Dianne Feinstein, D-California, is pushing legislation to reinstate a ban on assault weapons.
A former Marine's passionate disagreement with Feinstein has garnered attention online.
"I own the guns I own because I acknowledge mankind's shortcomings instead of pretending like they don't exist," Joshua Boston wrote in a CNN iReport. "There are evil men in this world and there just may be a time when I need to do the unthinkable to protect me or my family."
Facebook user Ellen Schmuker wrote in a CNN discussion that Giffords and Kelly's plan is "foolish" because "all gun bans are going to do is punish law abiding citizens for the actions of lunatics."
But HoaiPhuong Nguyen took the opposite stance. "No one is more qualified to head this effort, go Gabby and Mark," she wrote.
CNN.com users weighed in on Twitter as well, with Susan Blumberg-Kason saying she considers the idea "crucial."
'We can't be naive'
In their column Tuesday, Giffords and Kelly note that that gun violence "kills more than 30,000 Americans annually."
According to the Centers for Disease Control and Prevention, in 2009, 31,347 people died from firearm injuries. Nearly 60% were a result of suicide. Homicide comprised 37% of those deaths. Overall firearm injuries were down 2% from the year before.
Giffords' remarkable recovery after being shot in the head has inspired many across the political spectrum. She told ABC she's doing physical therapy, yoga, and speech therapy, and working with a service dog. She has also been able to begin some outdoor activities.