The video ends with the militant standing over a severed head he says belongs to Kassig. US officials said they were working to determine the video's authenticity. Kassig's family said it was awaiting the outcome of the investigation.
"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.
The video identifies the militants' location as Dabiq, a town in northern Syria that the Islamic State group uses as the title of its English-language propaganda magazine and where they believe an apocalyptic battle between Muslims and their enemies will take place.
The slickly produced video shows the beheadings of about a dozen men identified as Syrian military officers and pilots, all dressed in blue jumpsuits. The main militant in the video who speaks to the camera has a British accent and warns that US soldiers will meet a similar fate.
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A US-led coalition is targeting the Islamic State group in airstrikes, supporting Western-backed Syrian rebels, Kurdish fighters and the Iraqi military.
Audio in the video appears to have been distorted to make it more difficult to identify the militant. Previous videos featured a militant with a British accent that the FBI says it has identified, though it hasn't named him publicly.
Later, the militant claims Kassig was killed because he "fought against the Muslims in Iraq, while serving as a soldier." Kassig, from Indianapolis, Indiana, formerly served in the US Army's 75th Ranger Regiment, a special operations unit, and deployed to Iraq in 2007.