Earlier, a video appearing on a website thought to be affiliated with groups sympathetic to Jordanian-born fugitive Abu Musab al-Zarqawi, identified the captive as Eugene Armstrong and showed a masked man cutting his head off with a knife.
The US official said Armstrong's body had been recovered in Iraq, but did not specify where or when this happened.
The video showed the banner of the Tawhid and Jihad group, which said it had seized Armstrong along with another American and a British national and set a 48-hour deadline on Saturday to kill them.
In the video, five armed and masked men stood around the hostage, who was dressed in an orange overall typically worn by Muslim detainees in the US prison at Guantanamo Bay.
Tawhid and Jihad, in a video posted on the internet on Saturday, said it would slit the throats of Armstrong, American Jack Hensley and the British Kenneth Bigley - unless Iraqi women were freed from Abu Ghraib and Umm Qasr prisons by Monday.
The US military says no women are being held in the two prisons specified, except for two who are thought to have worked on an illicit weapons programme.