In a video statement the previously little known group, Katibat al-Fursan (The Knights Brigades), said it had given repeated warnings that dealings with the US forces should stop, but to no avail.
It said this would be the last warning before "just vengeance" would be imposed on the three abducted workers.
Turkey borders Iraq to the north, and its nationals have frequently been killed in the persistent violence in the war-torn country.
Around 90 Turks have been killed in recent months, most of them truck drivers caught in ambushes.
Many Turkish drivers have also been kidnapped in northern Iraq in the past, but most have been released.