When the radio host noted that expanding background checks is supported by roughly 90 percent of Americans, McConnell acknowledged that "there's a lot of support for that."

ADVERTISEMENT

McConnell did not say whether he supports expanding background checks or that he would give a bill that expands background checks a vote as part of the Senate's upcoming debate.

The Senate has been a consistent roadblock to expanding background checks after a failed 2013 vote on the Manchin-Toomey proposal. Senators voted 54-46 on the proposal, falling short of the 60 vote threshold.

McConnell predicted on Thursday that other issues, including questions about assault weapons, would also likely come up.

"That will probably be discussed as well. We had that ban for about a 10-year period," he said. "Background checks and red flags would probably lead the discussion, but a lot of other things will come up as well. What we can't do is fail to pass something."

McConnell is facing intense pressure from Democrats to bring the Senate back into session during the August recess to vote on a House-passed bill, which would go further than Manchin-Toomey by implementing universal background checks.

That bill has no chance of passing the Senate after clearing the House with the support of eight Republicans. The Senate's companion bill has 42 co-sponsors, none of whom are Republicans.

McConnell rejected calls on Thursday to bring the chamber back , saying senators and their staffs would use the five-week break to discuss what can pass the Senate.