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Mr. Cameron also called Tuesday’s beheading an “absolutely disgusting, despicable act.”

Analysts say the Islamic State knows that such brutal acts, and releasing video of those acts, spark outrage and can prompt a more vigorous international response. But the organization relies on the method for a variety of purposes, according to William McCants, director of the Project on U.S. Relations with the Islamic World at the Brookings Institution.

“ISIS is keenly aware that its beheadings are bad for public relations. Al Qaeda’s senior leaders have cautioned them against the stunt for years. But ISIS doesn’t care,” he said.

Mr. McCants said the Islamic State even hopes to anger the American public, and thereby influence U.S. foreign policy into choices it favors.

“The insurgent group is using the beheadings to communicate to the United States and its allies that it can respond to their attacks. It also wants to rile the American public so [that] it [then] puts pressure on the Obama administration to commit ground troops or leave the theater. Either would be a win in the eyes of ISIS.”