WASHINGTON — Shifting the gun violence debate, Senate Majority Leader Mitch McConnell said Thursday he now wants to consider background checks and other bills, setting up a potentially pivotal moment when lawmakers return in the fall.

The Republican leader won’t be calling senators back to work early, as some are demanding. But he told a Kentucky radio station that President Donald Trump called him Thursday morning and they talked about several ideas. The president, he said, is “anxious to get an outcome and so am I.”

Stakes are high for all sides, but particularly for Trump and his party. Republicans have long opposed expanding background checks — a bill passed by the Democratic-led House is stalled in the Senate — but they face enormous pressure to do something after mass shootings in El Paso, Texas and Dayton, Ohio, that killed 31 people. McConnell, who is facing protests outside his Louisville home, can shift attention back to Democrats by showing a willingness to engage ahead of the 2020 election.

“What we can’t do is fail to pass something,” McConnell said. “What I want to see here is an outcome.”

McConnell said he and Trump discussed various ideas on the call, including background checks and the so-called “red flag” laws that allow authorities to seize firearms from someone deemed a threat to themselves or others.

“Background checks and red flags will probably lead the discussion,” McConnell told WHAS-AM in Louisville. He noted “there’s a lot of support” publicly for background checks. “Those are two items that for sure will be front and center as we see what we can come together on and pass.”

Trump has been interested in federal background checks before — and tweeted Monday about them — only to drop the issue later, a turnaround similar to his reversal on gun proposals after the 2018 high school shooting at Parkland, Fla.

The powerful National Rifle Association and its allies on Capitol Hill have long wielded influence, but the gun lobby’s grip on Democrats started slipping some time ago, and it’s unclear how much sway the NRA and other gun groups still hold over Republicans in the Trump era.