GAZIANTEP, Turkey — Islamic State militants released a chilling videotape on Sunday showing they had beheaded a fifth Western hostage, an American aid worker the group had threatened to kill in retaliation for airstrikes carried out by the United States in Iraq and Syria.

President Obama on Sunday confirmed the death of the aid worker, Peter Kassig, a former Army Ranger who disappeared more than a year ago at a checkpoint in northeastern Syria while delivering medical supplies.

Mr. Kassig “was taken from us in an act of pure evil by a terrorist group,” Mr. Obama said in a statement from aboard Air Force One that was read to the news media in Washington.

In recent days, American intelligence agencies received strong indications that the Islamic State had killed Mr. Kassig, the group’s third American victim. The president’s announcement was the first official confirmation of his death.