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“We can’t let them get away with this. We have to stand up to them,” he said.

Rep. C.A. Dutch Ruppersberger of Maryland, the ranking Democrat on the House Permanent Select Committee on Intelligence, agreed that the government was taking appropriate action.

“We need to take every precaution necessary, and that’s what we’re doing right now,” Mr. Ruppersberger said on ABC’s “This Week.”

Rep. Peter T. King, New York Republican and past chairman of the House Committee on Homeland Security, said he often disagrees with the Obama administration on matters of national security but supports the steps officials have taken in recent days.

“They’d be derelict if they were not,” Mr. King said on “This Week.” “[A]s far as this worldwide alert, I think it’s absolutely warranted in this situation.”

Mr. McCaul said the State Department warning is significant because al Qaeda in the Arabian Peninsula is probably the biggest threat to the U.S.

“They’re the al Qaeda faction that still talks about hitting the West and hitting the homeland,” he said. “And their expertise is chemical explosives, hitting the aviation sector, as we saw with the underwear bomber. So we are on a high state of alert.”

Former NSA and CIA Director Gen. Michael V. Hayden said on “Fox News Sunday” that the terrorist threat is an indication that the danger posed by al Qaeda is not over.

“You have a real danger to Americans, you want to be cautious,” Mr. Hayden said. “The announcement itself might also be designed to interrupt al Qaeda planning, to put them … on the back foot, to let them know that we’re alert, and that we’re onto at least a portion of this plot line.”