For Mr. Trump, his dealings with Mr. LaPierre and other gun rights advocates in recent weeks have been a reminder that even if his initial instinct after the mass shootings this month was to say he would press for aggressive gun legislation, any such push would be seen as a betrayal of the N.R.A. members who helped elect him.

At the N.R.A.’s annual convention in 2017, Mr. Trump assured the group’s members, “You came through for me, and I am going to come through for you.” And that is what he was doing on his call with Mr. LaPierre, according to two people familiar with their conversation, assuring Mr. LaPierre that even after another round of mass shootings, he was not interested in legislation establishing universal background checks and that his focus would be on the mental health of the gunmen, not their guns.

Mr. Trump — who did most of the talking on the call with Mr. LaPierre, according to those briefed on the conversation — made it clear that he thinks there are ways to scrutinize people’s fitness for gun ownership other than the current proposals. But his latest comments on guns were the strongest sign to date that he is unlikely to make bipartisan gun legislation a priority this fall, when Congress returns from its summer recess. Without his backing, congressional Republicans said, any chance of a bipartisan bill passing the Senate is likely to be dead on arrival.

Instead, the president told Mr. LaPierre that he wanted to focus on mental health and access to juvenile criminal records. Those measures fall far short of the sweeping new restrictions that Democrats sought and that Mr. Trump said he was prepared to endorse in the immediate aftermath of the mass shootings on Aug. 3 and 4 that left more than 30 dead.

The president’s remarks also demonstrated how the N.R.A., which spent $30 million on Mr. Trump’s campaign in 2016 and stuck with him when other Republicans wavered in their support, still wields great influence over the White House, even as its own future is in question. The organization has been mired in investigations into its finances by two attorneys general, in New York and Washington, as well as a legal battle with its former advertising firm and calls from its own board members for change.