Abdul-Rahman Kassig: US hostage 'killed by IS'
The video shows a masked man standing over a severed head which he says is that of Mr Kassig.
The US says it is working to determine the authenticity of the video, which also shows a mass beheading of 18 Syrian troops.
Mr Kassig, also known as Peter, was captured last year.
His family, who live in the US state of Indiana, said they were awaiting confirmation of the reports about their "treasured son".
"We prefer our son is written about and remembered for his important work and the love he shared with friends and family, not in the manner the hostage takers would use to manipulate Americans and further their cause," the family said in a statement.
BBC
