Senate Majority Leader Mitch McConnell (R-Ky.), shown July 23 on Capitol Hill, mentioned in an interview expanding background checks on gun purchases and “red-flag” laws as possible legislative actions the Senate could take to address gun violence. (Susan Walsh/AP)

Senate Majority Leader Mitch McConnell said Thursday he spoke to President Trump about the Senate working on legislation to tighten the nation’s gun laws after the August recess, as both men face heightened public pressure to do something about gun violence following last weekend’s two mass shootings.

The Kentucky Republican, in his first interview since the shootings left 31 dead and dozens injured, specifically mentioned expanding background checks on gun purchases and “red-flag” laws, which would allow authorities to confiscate a firearm from someone deemed a risk to themselves or the public.

“Those are two items that will be front and center as we see what we can come together on and pass,” McConnell said on Kentucky radio station 840 WHAS.

At the same time, McConnell, who faces reelection next year, underscored the difficulty in reaching consensus on a divisive issue. Congress has not passed significant gun-control legislation since the 1990s.

“It’s always a challenge in making federal legislation because we do have a lot of differences in our country over an issue like this,” he said. “I mean, how people in South Dakota, for example, feel about this issue would be dramatically different from how they feel about it in Boston.”

McConnell, who is recuperating from a fractured shoulder, said he spoke to Trump on Thursday.

Democrats have been urging McConnell to bring the Senate back to Washington immediately to vote on a measure that House passed in February to expand background checks on firearm sales. House Speaker Nancy Pelosi (D-Calif.) sent a letter Thursday to Trump asking him to use his constitutional powers to force the Senate back into session to vote on the bill.

“Mr. President, we have an opportunity to work in a bipartisan way to pass gun violence prevention background checks. However, Leader Mitch McConnell, describing himself as the ‘grim reaper,’ has been an obstacle to taking any action,” Pelosi wrote.

Pelosi and Senate Minority Leader Charles E. Schumer (D-N.Y.) said in a joint statement that they’d spoken to Trump by phone on Thursday about gun policy.

“We spoke to the President separately this afternoon and told him the best way forward to address gun violence in our country is for Leader McConnell to let the Senate take up and pass the House-passed universal background checks legislation and for the President to sign it into law,” they said. “The President gave us his assurances that he would review the bipartisan House-passed legislation and understood our interest in moving as quickly as possible to help save lives.”

McConnell has been steadfast that he wouldn’t bring up anything unless it had Trump’s support and could garner a filibuster-proof 60 votes. Trump had threatened to veto the House-passed bill, but has signaled this week a willingness to expand background checks.

McConnell described Trump as “anxious to get an outcome.”

“And so am I,” McConnell said. “And I believe the Democrats will have to just admit that 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.”

Trump has spoken to National Rifle Association chief executive Wayne LaPierre at least three times since the shootings and has been telling people he can get the NRA on board with something, according to administration officials who spoke on the condition of anonymity to describe private conversations. LaPierre said in a statement he wouldn’t discuss what he and Trump spoke about privately.

“But I can confirm that the NRA opposes any legislation that unfairly infringes upon the rights of law-abiding citizens,” he said. “The inconvenient truth is this: the proposals being discussed by many would not have prevented the horrific tragedies in El Paso and Dayton. Worse, they would make millions of law abiding Americans less safe and less able to defend themselves and their loved ones.”

LaPierre continued: “The NRA will work in good faith to pursue real solutions to the epidemic of violence in America. But many proposals are nothing more than ‘sound bite solutions’ — which fail to address the root of the problem, confront criminal behavior, or make our communities safer.”

The Senate last attempted to pass new gun laws a few months after the December 2012 Sandy Hook Elementary School massacre in Newtown, Conn. A bipartisan effort involving Sens. Joe Manchin III (D-W.Va.) and Patrick J. Toomey (R-Pa.) on a background checks bill gave the legislation its best chance at passing in years, but it ultimately fell short by six votes.

There is talk of resurrecting the Manchin-Toomey bill, which closes loopholes in background check laws and is similar to a measure passed in the House this year. But gun-control advocates prefer the House version because the senators included some concessions to gun rights advocates, such as providing exceptions for sales between family members.

Sens. Lindsey O. Graham (R-S.C.) and Richard Blumenthal (D-Conn.) have said they are working on a red-flag bill that would offer federal grants and other incentives for states to develop laws implementing emergency risk protection orders. Those statutes would allow family members, law enforcement officials and others to petition a judge to bar firearms from someone they believe is an imminent threat to themselves or others. Seventeen states and the District already have such laws on the books, according to the Giffords gun-control group.

“What we can’t do is fail to pass something, you know, by just locking up and failing to pass — that’s unacceptable,” McConnell said. “What I want to see here is an outcome, not a bunch of partisan back-and-forth, these shots across the bow.”

Mike DeBonis and Josh Dawsey contributed to this story.