"The president called me this morning about this. He's anxious to get an outcome and so am I, and I believe the Democrats will have to admit it's better to get a result than just engage in this sort of endless point-scoring that has the tendency to occur after one of these awful, awful incidents," McConnell said.
McConnell said he doesn't see a point in calling the Senate back into session, despite numerous calls from Democrats to do so.
"We'd just have people scoring political points and nothing would happen," McConnell said.
But he is on board with passing some sort of legislation in September that has bipartisan support in both chambers of Congress, as well as the president's buy-in.
It's unclear what that legislation would look like. But McConnell acknowledged in the radio interview that background check legislation will be "front and center" when Congress returns from recess in September.
“Background checks and red flags will probably lead the discussion," McConnell said. "Those are two items that for sure will be front and center as we see what we can come together on and pass."
The House passed two background-check bills in February but the Senate has, so far, failed to act.
Senate Minority Leader Chuck Schumer and House Speaker Nancy Pelosi said in a statement that they had spoken by phone to Trump and that he had given his "assurances" that he would review the House legislation.
One of the bills would establish new background check requirements for firearm transfers between private parties. The other bill would extend the review period for the FBI to complete its background check for gun purchases from three days to 10 days.
Congress has not passed any sweeping gun reform legislation since the 1990s. Lawmakers have tried and failed numerous times, most notably after the 2012 shootings in Newtown, Connecticut, in which 20 school children were killed by a gunman.
While Congress has failed to reach a bipartisan consensus on broad gun control legislation and the House-passed background check bills wait in the Senate, some senators are working on other legislation to address the gun violence epidemic.
Republican Sen. Lindsey Graham, a top Trump ally, announced in a statement on Monday that he and Democratic Sen. Richard Blumenthal of Connecticut had reached an agreement on a federal grant program that would assist states in implementing a "red flag" law.
The state law typically permits police or family members to petition a state court to order the temporary removal of firearms from a person who may present a danger to others or themselves.
Graham said he spoke to Trump on Monday morning and that the president seemed "very supportive" of the idea.
Trump also spoke to another bipartisan duo on Monday -- Sens. Pat Toomey, R-Pa., and Joe Manchin, D-W.Va. -- about a separate piece of legislation that would expand background checks for unlicensed gun show purchases and online sales.
"This morning, we both separately discussed with President Trump our support for passing our bipartisan legislation to strengthen background checks to keep guns out of the hands of criminals, the dangerously mentally ill, and terrorists, while respecting the Second Amendment rights of law-abiding gun owners and all Americans. The president showed a willingness to work with us on the issue of strengthening background checks," Manchin said in a statement.
Toomey said in a tweet that it is "time for Congress to act."
McConnell reiterated that he's counting on the Republican chairmen of certain Senate committees to reach out to not only their GOP colleagues, but to Democrats as well, to reach some sort of consensus on how to move forward on the issue of guns.
"We're going to have these bipartisan discussions," McConnell said. "And when we get back, hopefully, be able to come together and actually pass something. I want to make a law, not just see this kind of political sparring going on endlessly which never produces a result."