The US military earlier reported that one of its helicopters had crashed while on patrol south-west of Baghdad.
The fate of the crew was not known.
A group calling itself the Al-Rashideen Army made the claim on the internet.
The authenticity of the message could not be confirmed.
Meanwhile, speaking on a visit to the north-west of England, US Secretary of State Condoleezza Rice said America had no desire to be "the world's jailer" and did not want to keep the Guantanamo Bay detention centre open any longer than is needed.