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President Obama declared Monday that his administration "will not rest" until it tracks down everyone involved in the attempted bombing of a Detroit-bound flight on Christmas, and pledged to do "everything in our power" to ensure security in the thick of the holiday travel season.

In his first public remarks on the incident, the president said Americans should be "confident," but also stay "vigilant."

Obama, who is on vacation in Hawaii, called the Detroit incident a "serious reminder" of the threat posed by terrorism abroad.

"A full investigation has been launched into this attempted act of terrorism and we will not rest until we find all who are involved and hold them accountable," Obama said. "Had the suspect succeeded in bringing down that plane, it could have killed nearly 300 passengers and crew, innocent civilians preparing to celebrate the holidays with their family and friends."

Al Qaeda in the Arabian Peninsula has claimed to be behind the attempted strike. Suspect Umar Farouk Abdulmutallab is now in custody -- he allegedly tried to set off an explosive mixture, but the chemicals did not detonate and he was subdued by other passengers.

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The president said Monday that he's taken several steps in response to the incident. He ordered immediate added security measures at airports and ordered a review of terror watch lists and security protocols at airports. The suspect was on a broad federal database of people with known or suspected ties to terrorists but was not on a "no-fly" list.

"It's absolutely critical that we learn from this incident, take the necessary measures to prevent future acts of terrorism," Obama said.

At the same time, the president pledged to sustain his administration's expanded war on terrorism and made clear that he does not consider that front limited to Afghanistan.

"We will continue to use every element of our national power to disrupt, dismantle and defeat the violent extremists who threaten us, whether they are from Afghanistan or Pakistan, Yemen or Somalia or anywhere, where they are plotting attacks against the U.S. homeland," he said.

Several critics have questioned why the president took three days to speak to the public on the nearly successful terror attack.

"We're now, what, 72 hours into this and the president has not spoken, the vice president has not spoken, the attorney general has not spoken and (Homeland Security Secretary) Janet Napolitano has now told two different stories in two days," Rep. Peter King, R-N.Y., said Monday morning.

He compared the administration's communications effort to an "iron curtain."

"It's very hard, even for me being on the Homeland Security Committee and the intelligence committee, to get any information out of this administration," King said.