Giffords, the target of a shooting rampage in early January 2011, and Kelly, made the call on Wednesday at a press conference at the Safeway in Tucson, Ariz., where Giffords was shot.
Giffords spoke briefly at the event saying that Congress should be "bold, be courageous, please support background checks."
Giffords and Kelly were accompanied by a number of victims of the Tucson shooting.
Kelly also specifically urged Arizona Sens. John McCain (R) and Jeff Flake (R) to support universal background checks.
"Now Sens. Jeff Flake and John McCain are considering this legislation," Kelly said. "And I think it's clear to them that 92 percent of Americans support a universal background check. We think that number is near 90 percent for Arizonans."
Americans for Responsible Solutions, a new gun control group run by Giffords and Kelly, have recently begun airing aids pressuring Republican lawmakers to back universal background check legislation. The ads target Flake and Sen. Chuck Grassley (R-Iowa).
The push by Americans for Responsible solutions come as bipartisan a group of senators continue to try to compromise on background check legislation. Those negotiations seem to have slowed recently as the lawmakers argue over how to enforce the background checks for private private gun sales.
A number of legislators and President Obama have also called on Congress to reinstate a federal ban on assault weapons. Kelly said he supports an assault weapons ban but the focus right now should be on passing universal background checks.
"I don't see any role for that in our society," Kelly said when asked about assault weapons. "But the thing that we can do right now today, the thing that has momentum, the bill that can get through the Senate and hopefully through the House is a universal background check bill. Now there's certainly some changes to that, amendments maybe but that's the thing that we need to focus on right now."