The legislations concerned are about expanding background checks for gun purchase, which were already approved by the House, Xinhua news agency reported.
The letter signed by 214 members of the US Conference of Mayors sent to McConnell and Senate Democratic leader Chuck Schumer earlier on Thursday said: "The tragic events in El Paso (Texas) and Dayton (Ohio) this weekend are just the latest reminders that our nation can no longer wait for our federal government to take the actions necessary to prevent people who should not have access to firearms from being able to purchase them."
After rejecting the letter, McConnell said on Thursday night an interview with Kentucky radio station WHAS: "We're going to have these bipartisan discussions and when we get back (from the summer recess), hopefully, (we'll) be able to come together and actually pass something."
"Background checks and red flags will probably lead the discussion.
"Those are two items that for sure will be front and centre as we see what we can come together on and pass."
The Democratic-led House passed two gun bills in February.
One is aimed at closing loopholes that have allowed some sales over the Internet and at gun shows to be finalized without background checks, and the other would extend to 10 business days, from the current three, the amount of time for background checks if information on a gun sale application is incomplete.
In a joint statement, Schumer and House Speaker Nancy Pelosi said President Donald Trump called them individually on Thursday, assuring them that he will review the House-passed gun bills.
( With inputs from IANS )