Middle East
16 November 2014
Last updated at 16:29 ET
The video, authenticated by the White House, shows a masked man standing over Mr Kassig's severed head. It also shows the beheading of 18 Syrian captives.
Mr Kassig, 26, is the fifth Western hostage to be killed by IS, which controls large parts of Syria and Iraq.
He was abducted in Syria last year while delivering relief supplies to refugees.
The president praised Mr 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 grieve together, yet we also recall that the indomitable spirit of goodness and perseverance that burned so brightly in Abdul-Rahman Kassig," he said.
Mr Obama's comments came as he flew back to the US from Australia where he was attending the G20 summit.
Ed and Paula Kassig have said earlier they did not want their son's death to be manipulated by the hostage takers
A photograph of Abdul-Rahman with his father, Ed, fishing on the Ohio River in Indiana in 2011
'British' jihadist
IS, which controls large parts of Syria and Iraq, has now murdered five Western hostages.
The others were Britons Alan Henning and David Haines, and US journalists James Foley and Steven Sotloff.
Those killings were carried out by a man believed to be British. That man bears a resemblance to one of the masked militants pictured in the video showing Mr Kassig.
Unlike previous videos released by IS, the latest one shows the faces of many of the jihadis and specifies its location - Dabiq in Syria's Aleppo province.
Mr 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) organisation, helping to supply camps on both sides of the Syrian border.
He was undertaking a project for Sera when he was captured in October 2013 while travelling to eastern Syria.
by Melissa Gruz and Biodun Iginla, BBC News Website
The 26-year-old American was captured last year
President
Barack Obama has confirmed the death of US aid worker Abdul-Rahman
Kassig, whose beheading was shown in a video posted by Islamic State
(IS).
Mr Obama called the act "pure evil" and offered condolences to his relatives.The video, authenticated by the White House, shows a masked man standing over Mr Kassig's severed head. It also shows the beheading of 18 Syrian captives.
Mr Kassig, 26, is the fifth Western hostage to be killed by IS, which controls large parts of Syria and Iraq.
He was abducted in Syria last year while delivering relief supplies to refugees.
The president praised Mr 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 grieve together, yet we also recall that the indomitable spirit of goodness and perseverance that burned so brightly in Abdul-Rahman Kassig," he said.
Mr Obama's comments came as he flew back to the US from Australia where he was attending the G20 summit.
Ed and Paula Kassig have said earlier they did not want their son's death to be manipulated by the hostage takers
A photograph of Abdul-Rahman with his father, Ed, fishing on the Ohio River in Indiana in 2011
The others were Britons Alan Henning and David Haines, and US journalists James Foley and Steven Sotloff.
Those killings were carried out by a man believed to be British. That man bears a resemblance to one of the masked militants pictured in the video showing Mr Kassig.
Unlike previous videos released by IS, the latest one shows the faces of many of the jihadis and specifies its location - Dabiq in Syria's Aleppo province.
Mr 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) organisation, helping to supply camps on both sides of the Syrian border.
He was undertaking a project for Sera when he was captured in October 2013 while travelling to eastern Syria.
Islamic State
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From other news sites
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Hindustan Times Peter Kassig beheading US review of IS video confirms Americans death 25 mins ago
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Los Angeles Times Islamic State beheaded U.S. aid worker Peter Kassig, White House confirms 1 hr ago
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Reuters UK Beheading of U.S. hostage 'an act of pure evil' - Obama 1 hr ago
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ABC News White House Confirms Death of US Aid Worker in ISIS Video
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