Reuters could not immediately verify the authenticity of the footage, which appeared on a jihadist website and on Twitter feeds used by Islamic State.
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Kassig, a 26-year-old from Indiana, is also known as Abdul-Rahman, a name he took following his conversion to Islam while in captivity.
Kassig's parents have said through a spokesperson their son was taken captive on his way to the eastern Syrian city of Deir al-Zor on Oct. 1, 2013.
A former soldier, Kassig was doing humanitarian work through Special Emergency Response and Assistance, an organization he founded in 2012 to help refugees from Syria, the family has said.
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If confirmed, Kassig's beheading would be the fifth such killing of a Westerner by Islamic State, following the deaths of two U.S. journalists and two British aid workers.
In an apparent reference to testimony about Kassig by former fellow captives, the masked man says: "Peter, who fought against the Muslims in Iraq while serving as a soldier under the American army, doesn't have much to say. His previous cellmates have already spoken on his behalf."
The announcement of Kassig's death formed part of a 15-minute video in which the group issued warnings to the United States, Britain and others including Shi'ite Muslims.
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It also shows militants beheading several men identified as pilots and officers loyal to Syrian President Bashar al-Assad.
"To Obama, the dog of Rome, today we are slaughtering the soldiers of Bashar and tomorrow we will be slaughtering your soldiers," the masked militant said.
British Prime Minister David Cameron said he was horrified by the "cold-blooded murder". Britain's Foreign Office said it was analyzing the video.