Barack Obama called the act “pure evil” and offered his condolences to the family of Abdul-Rahman Kassig, 26.
Abdul-Rahman Kassig, also known as Peter Kassig, was abducted in Syria last year.
The video, authenticated by the White House, shows a masked man standing over Abdul-Rahman Kassig’s severed head.
It also shows a beheading of 18 Syrians identified as army officers and pilots.
The president praised Peter Kassig as a humanitarian and said he was “taken from us in an act of pure evil by a terrorist group that the world rightly associates with inhumanity”.
“Today we offer our prayers and condolences to the parents and family of Abdul-Rahman Kassig, also known to us as Peter,” he added.
Barack Obama’s comments came as he flew back to the US from Australia where he was attending the G20 summit.
Peter Kassig was a former US Army Ranger who served in Iraq.
He later trained as an emergency medical technician and founded the Special Emergency Response and Assistance (SERA) organization, helping to supply camps on both sides of the Syrian border.
Peter Kassig was undertaking a project for SERA when he was captured in October 2013 while travelling to eastern Syria.
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