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The video, which appears not to have been broadcast widely on television, has generated ire among Democrats and gun control advocates who say it improperly drags the president's daughters into the national debate over guns.

Posted at a Web site called N.R.A. Stand and Fight, the video starts by asking, "Are the president's kids more important than yours?"

The video does not show Mr. Obama's daughters, Malia, 14, and Sasha, 11. But it suggests that Mr. Obama holds their safety to a different standard than he is willing to offer for other children in the country.

In a strongly worded statement, the White House press secretary Jay Carney lashed out at the N.R.A.

"Most Americans agree that a president's children should not be used as pawns in a political fight," Mr. Carney said. "But to go so far as to make the safety of the President's children the subject of an attack ad is repugnant and cowardly."

The N.R.A. video is a reference to Mr. Obama's stated skepticism about the group's idea to prevent school massacres by posting armed guards at every one of the nation's schools.

"I am skeptical that the only answer is putting more guns in schools," Mr. Obama said during a recent interview on the NBC News program "Meet the Press." "And I think the vast majority of the American people are skeptical that that somehow is going to solve our problem."

A week after the shootings at a school in Newtown, Conn., Wayne LaPierre, the chief executive and vice president of the N.R.A., held a news conference in which he called for more security in schools and an end to the "gun-free zones" that are common around many school buildings.

"The only thing that stops a bad guy with a gun is a good guy with a gun," Mr. LaPierre said at the time.