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Mr. Kelly, appearing on “Fox News Sunday,” said he would like Mr. LaPierre to “listen to his membership.”

“Seventy-four percent of NRA members think [background checks are] a very reasonable thing to do,” Mr. Kelly said.

Amid the back-and-forth on gun control this weekend, the White House on Saturday unexpectedly released a photo of Mr. Obama, gun to shoulder, getting in some target practice in a photo dated Aug. 4.

The president, in a recent interview with The New Republic, said he and guests at the presidential retreat in the Maryland mountains go skeet shooting “all the time,” prompting much online derision and outright skepticism.

Critics of the president contend that the comment and the photo are transparent attempts to ingratiate the president with gun owners.

The NRA, responding to the skeet-shooting photo, said: “One picture does not erase a lifetime of supporting every gun ban and every gun-control scheme imaginable.”