The Iraqi was one of five wounded prisoners left in the mosque after US marines had fought their way in on Friday and Saturday. There was no immediate comment from the Pentagon on the report.
US forces launched an offensive one week ago on Falluja, and claim to have gained overall control of the city, although resistance fighters dispute this.
The pool report by NBC correspondent Kevin Sites said the mosque had been used by fighters to attack US forces, who stormed it and an adjacent building, killing 10 fighters and wounding five.
Sites said the wounded had been left in the mosque for others to pick up and move to the rear for treatment. No reason was given why that had not happened.
Images too graphic
A second group of marines entered the mosque on Saturday after reports it had been reoccupied. Footage from the embedded television crew showed the five still in the mosque, although several appeared to be already close to death, Sites said.
He said one marine noticed one of the prisoners was still breathing.
A marine can be heard saying on the pool footage provided to Reuters Television: "He's [expletive] faking he's dead. He faking he's [expletive] dead."
Marines had left a group of
prisoners in the mosque
"The marine then raises his rifle and fires into the man's head. The pictures are too graphic for us to broadcast," Sites said. No images of the shooting were shown in the footage provided to Reuters.
The report said the marine, who had returned to duty after being shot in the face a day earlier, had been removed from the field and was being questioned by the US military.
Sites said the shot prisoner "did not appear to be armed or threatening in any way".