CAMP FALLUJAH, Iraq -- Iraqis are expressing outrage over the killing of a wounded and apparently unarmed Iraqi insurgent by a Marine in a Fallujah mosque.

Iraqi officials sought to dampen furor of the shooting, which could cause major political problems for Prime Minister Ayad Allawi. The interior minister said that while Iraqis don't believe in killing the wounded, the militants in Fallujah were "killers and criminals" who had committed brutal acts against Iraqis and foreigners.

But a man who works for the Iraqi Transportation Department said it made him want to scream. He said his wife was crying when she saw the shooting on TV and he had tears in his eyes.

A merchant said she's offended that such acts took place inside what she calls "God's house." Others called the shooting "criminal" and "cowardice."

The general in charge of Marines fighting in Fallujah said his troops hold themselves "to a high standard of accountability," and promises a full investigation.

The Marine involved in the fatal shooting has been pulled off the battlefield.

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Slideshow: Fatal Shooting Caught On Tape
Video: Watch Shooting Video

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The 1st Marine Expeditionary Force commander said the investigation is under way to determine whether the Marine acted in self-defense, violated military law or failed to comply with the law of armed conflict.

Lt. Gen. John Sattler said the facts of the case will be "thoroughly pursued" to protect the rights of everyone involved.

News video shows some Marines returning to a Fallujah mosque Saturday that they had stormed the day before. The tape shows a Marine raising his rifle toward a wounded prisoner on the floor of the mosque and then shouting expletives.

According to the tape shown on CNN, this is what follows:

"He's (expletive) faking he's dead!"
"Yeah, he's breathing," another Marine is heard saying.
"He's faking he's (expletive) dead!" the first Marine says.
The video is then blacked out and a rifle shot is heard.
"He's dead now," a Marine is heard saying.

Correspondent Kevin Sites said in a written report that four of the previously wounded prisoners had been shot again and one was dead.

Meanwhile, the International Committee of the Red Cross said it's trying to contact its representatives in Iraq to find out what they know about the shooting.

Protecting wounded combatants is a basic rule in the universally accepted Geneva Conventions.

The Red Cross is mandated to uphold those rules on warfare. And so far it says it won't comment until it learns more about the case.

A spokesman for the International Committee for the Red Cross said it's "not clear" whether the man was a prisoner and protected by the Geneva Conventions.

The Red Cross spokesman cautioned against a rush to judgment without a full investigation. But he said the Geneva Conventions are clear that wounded combatants must be protected.

A British defense analyst is defending the U.S. Marine after the shooting.

Charles Heyman said soldiers are taught that the enemy is "at his most most dangerous" when injured. Heyman said the enemy might have hidden firearms or explosives.

The NBC reporter says the man who was shot to death didn't appear to be armed or threatening in any way, and there were no weapons visible in the room.

Expert: Shooting Investigation Not Unlike Civilian Probe

As the Marines investigate the fatal shooting of a wounded man in a mosque in Fallujah, a law professor at the National War College is shedding light on what's involved in the investigation.

The professor specializes in the Geneva Conventions. He says it's not clear whether provisions dealing with the treatment of prisoners of war will come into play, because there is no proof that the man had been classified as a POW prior to his death.

Marine spokesmen in Iraq have referred to the man as an enemy combatant -- a quite different distinction without the same protections.

The War College professor says he expects the investigation to be much more clear cut, focusing instead on whether the Marine shot in self-defense or whether there were violations of the rules of engagement and the Uniform Code of Military Justice.

The professor asked not to be identified because the investigation is still under way.