The video was issued by the Islamic State in Iraq, an umbrella group of Iraqi fighter groups.
James Conway, US marines commandant-general, said his forces did not believe that the CH-46 Sea Knight helicopter, the Marine-version of the Chinook, was shot down.
US military officials said early indications were that the craft's loss was due to mechanical failure.
The Islamic State in Iraq issued a written claim of responsibility on Wednesday for the craft's downing and had promised a video would follow.
The video, entitled "the Hell of Christians and Apostates in Iraq", was posted on a web forum where fighter groups often post messages.
Its authenticity could not be independently confirmed.
The crash was the sixth by a US helicopter since January 20, at least four of them downed by ground fire.
An Iraqi air force officer on Wednesday also said the CH-46 had been shot down. Five marines and two navy medics were killed in the crash.
Though he said the CH-46 was not believed to have been shot down, Conway said on Wednesday that there was a new and troubling "intensity of effort" by fighters to attack helicopters.