Kassig, a US aid worker, "was taken from us in an act of pure evil by a terrorist group that the world rightly associates with inhumanity," Obama said in a statement issued by the White House.
In a video uploaded to social networks, a militant with his face concealed stands before a severed head that he says is that of Kassig's. The video also shows what appears to be the mass beheading of more than a dozen captured Syrian soldiers.
"Today, we offer our prayers and condolences to the parents and family of Abdul-Rahman Kassig, also known to us as Peter," Obama said. "We cannot begin to imagine their anguish at this painful time."
The president praised Kassig as "a humanitarian who worked to save the lives of Syrians injured and dispossessed by the Syrian conflict" and described his deeds as "selfless acts of an individual who cared deeply about the plight of the Syrian people".
"Today we grieve together, yet we also recall that the indomitable spirit of goodness and perseverance that burned so brightly in Abdul-Rahman Kassig, and which binds humanity together, ultimately is the light that will prevail over the darkness of ISIL," he said, using an alternate acronym of the group.
Kassig is the third US hostage killed by IS in less than three months. Previous American victims were journalists James Foley and Steven Sotloff.