The tape was attributed to three Iraqi groups and showed blindfolded captives sitting against a wall.
The channel said the men were working for a US security firm, but did not give its name.
The tape included a statement from the masked gunmen, images of the captives' belongings and a plea from one of them for Iraqis to stop cooperating with the US forces and the US-backed Iraqi administration.
"The company supplies tanks which are used in fighting," the blindfolded captive said. "I urge everyone not to work for the Americans or to help the government of [Iraqi interim prime minister] Iyad Allawi."
It was not clear when the men were seized, and the television stations did not say if the group had set a deadline to carry out its threat.
A man saying he represented the group told Reuters in Baghdad on Saturday he had a video that he said showed 10 drivers, most of them Iraqis.
He said the group was demanding their US company withdraw from Iraq.
Armed groups have frequently attacked contractors of various nationalities working for US-led forces in Iraq.