It has not been independently verified but has been released by Islamic State.
The 26-year-old was threatened at the end of a video showing the beheading of British aid worker Alan Henning in October after being captured by I.S. a year earlier.
Despite his Christian upbringing Mr Kassig converted to Islam after travelling to the Middle East as an aid worker.
He wanted to be known as Abdul-Rahman Kassig.
He founded SERA (Special Emergency Response and Assistance) which helps refugees with medical aid and it was whilst working for this organisation he was abducted.
His father, Ed Kassig, said he started the charity because of the influence of his grandfather who was a Methodist minister.
He said: "At an early age our son was inspired by his grandfather to do humanitarian work.
"When he saw the suffering of the Syrian people, he went to Turkey and founded an organisation to provide aid and assistance.
"He helped train 150 civilians in skills needed to provide medical aid to the people of Syria. This organisation gave food, cooking supplies, clothing and medicine to those in need.
"He grew to love and admire the Syrian people and felt at home there. Our son's journey culminated in him embracing Islam. Sadly, he was taken captive and is not free to continue his life's work serving the people of the region."
In October his mother, Paula Kassig, said: "We are so very proud of you and the work you have done to bring humanitarian aid to the Syrian people.
"Please know that we are all praying for you and your safe return."