The same video showed the gruesome simultaneous beheadings of at least 18 men described as Syrian military personnel, the latest in a series of mass executions and other atrocities carried out by IS.
In the undated video, a man who appears to be the same British-accented militant who beheaded previous Western hostages stands above a severed head.
“This is Peter Edward Kassig, a US citizen of your country,” the black-clad masked executioner says, urging US President Barack Obama to send more troops back to the region to confront IS.
“Here we are burying the first American crusader in Dabiq, eagerly waiting for the remainder of your armies to arrive,” the militant said, referring to a northern Syrian town.
There was no immediate confirmation from his family of the death of Kassig, a former US soldier who risked his life to provide medical treatment and aid to those suffering from Syria’s civil war.
Kassig would be the fifth Western hostage killed by IS in recent months, after two US reporters and two British aid workers.
British Prime Minister David Cameron said he was “horrified” by Kassig’s “cold-blooded murder”.
“ISIL have again shown their depravity. My thoughts are with his family, “Cameron wrote on Twitter, using an alternative name for IS.
The 26-year-old, who converted to Islam and took the first name Abdul-Rahman, was taken captive last year and was threatened in an October 3 video showing the beheading of British aid worker Alan Henning.
The claim of Kassig’s killing came as Washington prepares to double its military personnel in Iraq to up to 3,100 as part of the international campaign it is leading against IS.
The extremist group has seized control of large parts of Iraq and Syria, declared a “caliphate” and imposed its brutal interpretation of Islamic law.
The video released on Sunday also showed a highly choreographed sequence of the beheadings of at least 18 prisoners said to be Syrian officers and pilots loyal to President Bashar al-Assad.
The video shows militants marching the prisoners past a wooden box of long military knives, each taking one as they passed, then forcing them to kneel in a line and decapitating them.
Kassig’s parents had pleaded for his release, highlighting his humanitarian work and conversion to Islam.
Kassig had founded an aid group through which he trained some 150 civilians to provide medical aid to people in Syria. His group also gave food, cooking supplies, clothing and medicine to the needy.
He wrote to his parents saying: “If I do die, I figure that at least you and I can seek refuge and comfort in knowing that I went out as a result of trying to alleviate suffering and helping those in need.“
Sunday’s video was released as IS suffered battleground losses in Iraq backed by US-led air strikes.