"There's some senators, bipartisan, again, Senator Coburn and Senator Manchin and some others who are working on a package that I think that most of us will be able to support," McCain said on NBC's "Meet the Press." "I applaud their efforts."

McCain continued, "Obviously, we want to do everything we can to prevent guns from falling into the hands of people who are mentally unbalanced or criminals."

The bipartisan plan touted by McCain is currently under negotiation. Senators Tom Coburn (R-Okla.), Mark Kirk (R-Ill.), Joe Manchin (D-W.V.) and Chuck Schumer (N.Y.) have met to discuss the proposed legislation, which would close loopholes in the current background check system.