The Mujahedeen Shura Council made the claim in a video posted on the internet which showed the bodies of two of the soldiers attacked on June 16 near Youssifiyah, southwest of Baghdad, according to a statement on Tuesday by the SITE Institute, which monitors extremist websites.
The institute released still pictures from the video showing two of the American dead, one of whom had been decapitated.
According to the institute, the statement by the group said the video was released as "revenge for our sister who was dishonored by a soldier of the same brigade".
The nearly five-minute video shows the horribly mutilated bodies of the two soldiers, who had had their throats cut. The head of one of them was held high by an armed man, like a trophy. The head of the other was being stamped on by another armed man.
The video had extracts of old speeches by Osama bin Laden, the head of al-Qaeda, and Abu Mussab al-Zarqawi, the head of its Iraqi wing who was killed on June 7 by the US military.