HONOLULU — President Obama emerged from Hawaiian seclusion on Monday to try to quell gathering criticism of his administration’s handling of the thwarted Christmas Day bombing of an American airliner as a branch of Al Qaeda claimed responsibility.

“We will not rest until we find all who were involved and hold them accountable,” Mr. Obama told reporters during a break in his 10-day holiday vacation. “This was a serious reminder of the dangers that we face and the nature of those who threaten our homeland.”

He added that he had ordered reviews of the air navigation screening system and the terrorist watch list system. “The American people should be assured that we are doing everything in our power to keep you and your family safe and secure during this busy holiday season,” he said.

The president spoke after the branch of Al Qaeda in Yemen and Saudi Arabia claimed responsibility for the attempted attack and said it was in retaliation for recent American-backed attacks on its members in Yemen, according to the SITE Intelligence Group, which tracks militant Islamist Web sites.

In a statement issued on jihadist forums, Al Qaeda in the Arabian Peninsula boasted the success of the “Nigerian brother” in breaking through security barriers and of its own explosives technology, SITE reported. Federal authorities say Umar Farouk Abdulmutallab, a 23-year-old Nigerian, tried to set off explosives aboard a trans-Atlantic Northwest Airlines flight approaching Detroit on Friday.

The Qaeda branch blamed a technical fault for the low-power detonation, according to SITE. The group has mounted attacks within Yemen and Saudi Arabia, and in 2004 it captured and beheaded a 49-year-old American engineer working in Riyadh, Paul M. Johnson Jr.

Government terror experts said the Qaeda claim was apparently legitimate.

“The statement is certainly credible,” one government official said, “and it reflects this group’s growing desire to strike beyond the Arabian peninsula.”

Mr. Abdulmutallab has told federal authorities that he received training and materials from a bomb expert in Yemen associated with Al Qaeda.

The government of Yemen said in a statement on Monday that Mr. Abdulmutallab had been in Yemen this year from early August to early December “after obtaining a visa to study Arabic at a language institute.”

The statement, issued by the Yemeni embassy in Washington, said Mr. Abdulmutallab had a valid United States visa and other foreign visas. “There was nothing suspicious about his intentions to visit Yemen, especially considering he had also visited the U.S. in the past,” the statement said.

Questions about how Mr. Abdulmutallab slipped through the aviation security system have been compounded by the Obama administration’s assertion over the weekend that “the system worked,” a judgment it reversed Monday.

Just hours before the president’s appearance — his first public remarks since arriving in Hawaii on Thursday — Secretary of Homeland Security Janet Napolitano recalibrated the assessment she and another top official had offered on Sunday. Speaking on NBC’s “Today” show, Ms. Napolitano said her remark had been taken out of context and that the thwarted bombing in fact represented a failure of the nation’s aviation security system.

“Our system did not work in this instance,” she said. “No one is happy or satisfied with that. An extensive review is under way.”

Until now, Mr. Obama had tried to strike a balance between signaling that he is on top of the situation and not drawing more attention to it than it already was generating. Each day since Friday, his staff accompanying him here in his home state put out statements indicating that the president was holding conference calls and requesting action of government agencies. But he declined for three days to address it in public himself, cognizant perhaps of warnings by some terrorism experts against elevating such incidents and by extension their authors.

Yet the visual contrasts have been jarring. Pictures of passengers enduring tougher security screening at the airport were juxtaposed against images of the president soaking in the sun and surf of this tropical getaway. Appearing at a Marine base near the Kailua beachfront house he has rented, Mr. Obama on Monday praised the “quick and heroic actions of passengers and crew” but made no attempt to defend the security system that allowed the suspect onto the plane with explosives in the first place.

Beyond the reviews, he pledged unspecified action against any groups that were involved. “We will continue to use every element of our national power to disrupt, to dismantle and defeat the violent extremists who threaten us, whether they are from Afghanistan or Pakistan, Yemen or Somalia, or anywhere they are plotting attacks against the U.S. homeland,” Mr. Obama said.