WASHINGTON (CNN) -- His upcoming legislative push for tighter restrictions on firearms won't ignore the concerns of gun owners, President Barack Obama said in a wide-ranging interview published Sunday.

He pointed specifically to America's hunting and shooting tradition, which he said was also part of the tradition at Camp David, Md., the presidential retreat.

"Up at Camp David, we do skeet shooting all the time," Obama said in the interview with The New Republic. He was responding to a question about whether he had ever fired a gun.

While his teenage daughters haven't partaken in skeet shooting - a sport where participants fire shotguns to break airborne clay disks - he has brought guests with him, he said in the interview.

"I have a profound respect for the traditions of hunting that trace back in this country for generations," he said. "And I think those who dismiss that out of hand make a big mistake."

A week and a half ago, Obama signed 23 executive actions - which don't require congressional approval - to strengthen existing gun laws and take related steps on mental health and school safety.

He also called on Congress to reinstate an assault weapons ban that expired in 2004, to restrict ammunition magazines to no more than 10 rounds, and to expand background checks to include anyone buying a gun, whether at a store or in a private sale at an auction or gun show.

The moves came in response to the school shooting in Newtown, Conn., that left 27 people dead, including 20 children.

As part of the lead-up to Obama's gun control package, Vice President Joe Biden met with groups with a stake in the debate, including gun owner groups and organizations representing gun manufacturers.

That openness to hearing gun owners' points of view must continue as the debate moves to Congress, Obama said.

"So much of the challenge that we have in our politics right now is that people feel as if the game here in Washington is completely detached from their day-to-day realities. And that's not an unjustifiable view," he said.

But in his interview, Obama also suggested the reverse was true - that some gun owners were deaf to the arguments coming from advocates of tighter restrictions on firearms.

"Advocates of gun control have to do a little more listening than they do sometimes," he said.

Upcoming legislative battles, from gun control to increasing the federal debt ceiling, will be complicated if lawmakers are cowed by voices in the right-wing media, Obama argued.

"One of the biggest factors is going to be how the media shapes debates. If a Republican member of Congress is not punished on Fox News or by Rush Limbaugh for working with a Democrat on a bill of common interest, then you'll see more of them doing it," he predicted.

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