After conversion during captivity, Kassig took the name Abdul-Rahman.
The former soldier had appeared at the end of a clip which showed the killing of the British Alan Henning by IS in October.
Mr Kassig had returned to the region as a charity worker, after serving in Iraq in 2007.
Kassig, 26, was captured on October 1, 2013, by Islamic State (formerly ISIS/ISIL) militants. He had served in Iraq before becoming a medical technician. In May 2012, he travelled to Lebanon where he volunteered in hospitals.
His parents, Ed and Paula Kassig from Indiana, recorded a video message in May 2014 appealing for their son’s release.
“As Muslims around the world, including our son Abdul-Rahman Kassig, celebrate Eid al-Adha, the faith and sacrifice of Ibrahim, and the mercy of Allah, we appeal to those holding our son to show the same mercy and set him free,” they said in a statement.
Kassig founded his own aid organization, SERA (Special Emergency Response and Assistance), a non-governmental group intended to provide relief to Syrian refugees.