"Up at Camp David, we do skeet shooting all the time," Obama said, answering a question about whether he had fired a gun before. He said that his daughters had not participated but that he has "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."
The caption accompanying the official White House photo says it was taken at Camp David - the Maryland presidential retreat - on August 4, 2012, his 51st birthday.
Obama's answer drew skeptical reviews from Republicans, including Rep. Marsha Blackburn, R-Tennessee, who spoke Monday on CNN's "Erin Burnett OutFront."
"If he is a skeet shooter, why have we not heard of this? Why have we not seen photos? Why hasn't he referenced this at any point in time?" Blackburn said.
Then she issued something of a challenge to the president: "I think he should invite me to Camp David, and I'll go skeet shooting with him, and I bet I'll beat him."
White House Press Secretary Jay Carney told CNN's Jessica Yellin at Monday's briefing for reporters that Obama goes "to Camp David with some regularity, but I'm not sure how often he's done that" sport, which involves shooting clay discs with a shotgun.
He was also asked whether there were any photos, and if one could be provided to reporters.
"There may be, but I haven't seen it," he said.
Carney added, "When he goes to Camp David, he goes to spend time with his family and friends and relax, not to produce photographs.”
Carney said on Wednesday that he had no reaction to Blackburn's comments.
Reporters are not typically permitted to cover Obama's personal activities at the secluded retreat.
The release comes as Obama is advancing a slate of measures he says will prevent gun violence, including reinstituting an assault weapons ban, limiting the size of gun magazines, and requiring background checks on all gun sales. He also signed a series of executive actions relating to gun violence.
While the assault weapons ban has its proponents on Capitol Hill, some members of Congress are skeptical it will pass, considering Republican opposition and wary Democrats who represent conservative districts and states.
Vice President Joe Biden led Obama's gun violence task force convened after the December 14 shooting at an elementary school in Newtown, Connecticut.
He acknowledged to reporters after a Thursday meeting with Democrats on Capitol Hill that "Nothing we are going to do is fundamentally going to alter or eliminate the possibility of another mass shooting or guarantee that we will bring gun deaths down." Obama had made similar comments earlier in the month.
The president will take his gun-related platform on the road to Minnesota on Monday.
National Rifle Association spokesman Andrew Arulanandam reacted to the photo, telling CNN, "One picture does not erase a lifetime of supporting every gun ban and every gun control scheme imaginable."
– CNN's Gregory Wallace, Shirley Henry, Ashley Killough and Kevin Liptak contributed to this report