The six men were shown in the video footage posted on the internet on Thursday identifying themselves and saying they worked for the Jordanian Al-Daud firm "which deals with US forces".
The men said they regretted their action and had repented, but a statement by the Army of Ansar al-Sunna, which claimed their execution, said their repentance had come too late.
The sound of gunfire is then heard on the video amid cries of "Allahu Akbar" (God is greatest), but the picture is unclear, as was the number of people seen at a distance bowing down.
The footage also showed two men from the waist down moving about, presumably doing the shooting. A gun was seen in the hand of one of them.
The video was presented as the work of the "information section of the Army of Ansar al-Sunna".
The statement accompanying the video said the six men had been ferrying goods, ammunition and weapons to and from US bases on behalf of the Jordanian firm, which is contracted to an American base in western Iraq.
"Where was your remorse when children, women and elderly and young men were being killed every day before your eyes by those with whom you worked?" the statement said, warning that anyone who worked with US forces would meet a similar fate.
Iraqi soldiers and a marine at a
US base west of Baghdad
The drivers had been captured after they left a US base west of Baghdad, an earlier website statement said.
It was not possible to verify the authenticity of either the statements or the video.
The Army of Ansar al-Sunna has claimed a string of attacks in Iraq, including the murders of foreign captives and Iraqis accused of collaborating with US-led forces.