The rare decision by the U.S. State Department to close more than a dozen embassies across the Muslim world Sunday follows the discovery of a serious threat from a branch of al Qaeda aimed at U.S. and Western interests, Joint Chiefs of Staff Chairman Gen. Martin Dempsey said during an exclusive interview with ABC News.

"There is a significant threat stream and we're reacting to it," Dempsey told ABC News' Martha Raddatz during the interview for "This Week," describing the threat as "more specific" than previous threats.

(Image Credit: ABC News)

ABC News reported Thursday that embassies across the Middle East and North Africa - including those in Egypt, Iraq and Kuwait - will close Sunday because of "a specific threat against a U.S. embassy or consulate."

The State Department today issued a global travel warning to all U.S. citizens around the world, alerting them to the "continued potential for terrorist attacks."

READ: Citing Al Qaeda Threat, U.S. Issues Global Travel Alert

Dempsey said the action the terrorist group might take was "unspecified," but added that the intent was clear.

"The intent is to attack Western, not just U.S. interests," he said.

See more of the interview with Army Gen. Martin Dempsey Sunday on "This Week."

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