He added that the experience with guns in rural America differed dramatically from that in urban America. “If you grew up and your dad gave you a hunting rifle when you were 10, and you went out and spent the day with him and your uncles, and that became part of your family’s traditions, you can see why you’d be pretty protective of that,” he said.

“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 added. “And that means that advocates of gun control have to do a little more listening than they do sometimes.”

Mr. Obama has proposed reinstating and strengthening an expired ban on new assault weapons and high-capacity magazines, expanding criminal background checks for nearly all gun sales except those within families, and cracking down on straw purchasers who buy firearms for others who would not be able to pass a background check. He also used his executive authority to try to improve the background check database and to revive government research into gun violence.

In the interview, Mr. Obama also expressed concern for the state of football in America, particularly at the college level, where there is no union to represent the interests of players.

“I’m a big football fan,” he said, “but I have to tell you, if I had a son, I’d have to think long and hard before I let him play football. And I think those of us who love the sport are going to have to wrestle with the fact that it will probably change gradually to reduce some of the violence.”