WASHINGTON (MarketWatch) -- President Barack Obama said Monday that his administration is doing "everything in our power" to protect Americans and that the government won't rest until it's found all who were involved in an attempt to blow up a Detroit-bound airplane on Christmas Day.

"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," Obama said in brief remarks to reporters in Hawaii, where he is vacationing with his family.

Obama's remarks came after Homeland Security Secretary Janet Napolitano acknowledged that the U.S. air-security system failed when Umar Farouk Abdulmutallab was allowed to board the Christmas Day flight from Amsterdam to Detroit.

"Our system did not work in this instance," Napolitano said on NBC's "Today" show about the incident, a day after declaring that the system worked as it was supposed to. Her remarks in that earlier interview were "taken out of context," she said.

Secretary of Homeland Security Janet Napolitano. Reuters

Abdulmutallab, 23, is in custody and faces federal charges in connection with allegedly hiding an explosive device on his body and trying to detonate it as a Northwest Airlines flight DAL, -0.09% approached Detroit.

The Associated Press, citing authorities, said the device instead burst into flames, and Abdulmutallab was subdued by passengers. The plane landed safely.

Al Qaeda in the Arabian Peninsula claimed responsibility for the attempted bombing, the AP reported.

Airline stocks traded broadly lower in the wake of the incident. See more on the action in airline-sector shares.

Over the weekend, Obama ordered a review of the databases used to track terrorism suspects and keep them off of airplanes. "I have ordered a thorough review, not only of how information related to the subject was handled, but of the overall watch list system and how it can be strengthened," he said Monday.

Obama also demanded a review of screening policies, technologies and procedures related to air travel, he said. "We need to determine just how the suspect was able to bring dangerous explosives aboard an aircraft and what additional steps we can take to thwart future attacks," said Obama.

Stewart Baker, former assistant secretary for policy at the U.S. Department of Homeland Security, said Obama's review will find problems with the current system.

"But the bigger failure is one of design," Baker said in an email. "Our airline screening system is mostly focused on finding dangerous stuff [and] not dangerous people, and that approach is rapidly losing its effectiveness. The president needs to ask for a review that allows his advisers to look at the second, bigger failure or we will simply be patching a threadbare suit."

The Wall Street Journal reported that Harold Demuren, head of the Nigerian Civil Aviation Authority, said Abdulmutallab had paid cash on Dec. 16 for the $2,831 roundtrip ticket from Lagos, Nigeria, to Detroit via Amsterdam.

Demuren said Abdulmutallab's ticket came from a KLM office in Accra, Ghana. The suspect checked in for his flight with only a small carry-on bag, the Journal reported.

On Sunday, Napolitano said, "One thing I'd like to point out is that the system worked." But on Monday she said that that comment referenced the system of notifying other flights and law-enforcement officials on the ground quickly after the suspect tried to blow up the plane.

She said an extensive review of the system is underway per Obama's instructions.

Rep. Bennie Thompson, chairman of House Homeland Security Committee, said the incident would be the focus of a hearing in January. "The committee will get to the bottom of what did and did not happen with Mr. Abdulmutallab and what security precautions need to take place in the future," said Thompson, D-Miss., in a statement over the weekend.

Meanwhile, as 2010 approaches, more Americans believe that there will be another terrorist attack in the U.S. in the next year. Seventy-nine percent of voters now think it's likely that there will be another attack, up from 49% who said the same thing at the end of August, according to a new Rasmussen Reports poll.