Obama released his official statement on the latest act of brutality by the terror group, while aboard Air Force One, on his return from the G20 summit in Brisbane, Australia.
Referring to Kassig by his Muslim name Abdul-Rahman Kassig, Obama told reporters: "We offer our prayers and condolences to the parents and family of Abdul-Rahman Kassig, also known to us as Peter. We cannot begin to imagine their anguish at this painful time."
Kassig had converted to Islam while in captivity.
Obama further praised Kassig as a humanitarian who lost his life "in an act of pure evil" by IS.
In the video released by IS on Sunday (16 November), Kassig's head is seen lying in the sand at the feet of an IS militant known by the name of "Jihadi John" who is seen holding a knife and saying:
"This is Peter Edward Kassig, a US citizen of your country. Peter, who fought against Muslims in Iraq, was serving as a soldier in the American army, does not have much to say. His previous cellmates have already spoken on his behalf."
The 15-minute video, Although The Unbelievers Dislike It, also shows several other hostages kneeling in the desert with uniformed men standing behind them.
Obama's confirmation comes after thorough examination by authorities following the release of the video by al-Furqan Media that is controlled by IS.