“Yes, in fact, up at Camp David, we do skeet shooting all the time,” Mr. Obama said.

“The whole family?” Mr. Foer asked.

“Not the girls,” he said, “but oftentimes guests of mine go up there. And I have a profound respect for the traditions of hunting that trace back in this country for generations. And I think those who dismiss that out of hand make a big mistake.”

Mr. Obama went on to say that the reality of guns in urban areas differs from that in rural areas. “So it’s trying to bridge those gaps that I think is going to be part of the biggest task over the next several months,” he said. “And that means that advocates of gun control have to do a little more listening than they do sometimes.”

The skeet-shooting comment caught many off guard because it is not something the president has talked about. While other presidents have used the skeet-shooting range at Camp David, database searches of Mr. Obama’s speeches and interviews turned up no mention of participating.

“I would refer you simply to his comments,” Jay Carney, the White House press secretary, told reporters who asked after the interview was published how often the president shoots. “I don’t know how often. He does go to Camp David with some regularity, but I’m not sure how often he’s done that.”

Asked why no one had seen a picture or heard about it before, Mr. Carney said, “Because when he goes to Camp David, he goes to spend time with his family and friends and relax, not to produce photographs.”

That did not satisfy the skeptics. The Washington Post’s “Fact Checker” column cast doubt on the claim, while Fox News quoted an unnamed person saying Mr. Obama had participated once during a Marine competition at Camp David but not “all the time.” Representative Marsha Blackburn, Republican of Tennessee, went on CNN to question the assertion.