The moment was captured by Kevin Sites, a freelance photographer embedded with US forces, who is on assignment for American news station NBC .
Mr Sites has also published stories and pictures from the Falluja offensive on his own website.
Much of his writing highlights the soldiers' enthusiam for combat.
"The marines are operating with liberal rules of engagement," he writes on 10 November.
He also quotes Staff Sgt. Mortimer: "'We're going to let loose the dogs of war. It will be hell,' he says, smiling after."
However, a sense of admiration also comes across in Mr Sites' reporting: "They are extremely likeable - these young marines - full of bravado and easygoing about the danger that surrounds them."
Much of the European press condemned the killing, with Spain's El Periodico condeming the action as a war crime. Sweden's Sydsvenska Dagbladet described the killing as an "abominable and completely indefensible act".
The mosque had earlier been used by insurgents as a base to attack US forces. The day before the killing, a marine was killed by explosives planted in a booby-trapped corpse.
The US military has removed the soldier that shot the injured insurgent and launched an investigation.
The film is the latest controversial footage to emerge from Iraq. Several clips have been circulated online since the start of the invasion which show US soldiers shooting apparently unarmed people.
Footage originally shown on Australian channel ABC on 11 November also shows a marine shooting an apparently injured insurgent.
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Senior Desk Editor - International News Desk
