Keith Maupin of Batavia, Ohio, was captured in April during an ambush on a convoy west of Baghdad. The Arab satellite station aired a video showing a blindfolded man sitting on the ground but did not show the killing.
The station said the militants had shot Mr Maupin and quoted a statement from a previously unheard of group as saying the soldier was killed because of US policy in Iraq and in revenge for what it described as their "martyrs" in Iraq.
Mr Maupin, 20, was among eight Americans, seven of them contractors, who disappeared after the attack on April 9. The bodies of four civilian employees of Kellogg Brown & Root were later found in a shallow grave near the site of the attack. The body of Sergeant Elmer Krause, of Greensboro, North Carolina, was found later.
One civilian driver, Thomas Hamill from Mississippi, escaped nearly a month later.
Meanwhile two Turkish workers, who have been missing since the beginning of this month, were confirmed kidnapped after a Turkish news agency yesterday released pictures of them at an undisclosed location. The picture, released by the Ihlas agency, showed two Turks identified as Murat Kizil and Soner Sercali squatting in front of five insurgents carrying heavy machine guns and rocket-propelled grenades.
It appeared to show Mr Sercali, an air conditioning repair man, and his co-worker Mr Kizil, apparently calm and holding up their IDs, with no indication that their life was in immediate danger.
The US military could not confirm whether Mr Maupin had been killed, but had alerted the family to the story. A senior defence official, speaking on condition of anonymity, told Reuters that the army notified the family of Mr Maupin "that there's a rumour al-Jazeera or an Arab network may have a tape of an execution, but we do not know if it's their son or not".
"We wanted to make sure they knew about it, since there was some media speculation out there. In the meantime, we have not found the young man, nor have we changed his casualty status. He is still listed as captured," the official said. "We don't know his fate."