Marines interviewed on Tuesday said they didn't see the shooting as a scandal, rather the act of a comrade who faced intense pressure during the effort to quell the insurgency in the city.
"I can see why he would do it. He was probably running around being shot at for days on end in Falluja. There should be an investigation but they should look into the circumstances," said Lance Corporal Christopher Hanson.
"I would have shot the insurgent too. Two shots to the head," said Sergeant Nicholas Graham, 24, of Pittsburgh, Pennsylvania. "You can't trust these people. He should not be investigated. He did nothing wrong."
The military command launched an investigation after video footage showed a U.S. Marine shooting a wounded and unarmed man in a mosque in the city on Saturday. The man was one of five wounded and left in the mosque after Marines fought their way through the area.
A pool report by NBC correspondent Kevin Sites said the mosque had been used by insurgents to attack U.S. forces, who stormed it, killing 10 militants and wounding the five. Sites said the wounded had been left for others to pick up.
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 close to death, Sites said.
He said a Marine noticed one prisoner was still breathing.
A Marine can be heard saying on the pool footage provided to Reuters Television: "He's fucking faking he's dead."
"The Marine then raises his rifle and fires into the man's head," Sites said.
NBC said the Marine, who had reportedly been shot in the face himself the previous day, said immediately after the shooting: "Well, he's dead now."
THOROUGH PROBE PROMISED
The Marine commander in Falluja, Lieutenant General John Sattler, said his men followed the law of conflict and held themselves to a high standard of accountability.
"The facts of this case will be thoroughly pursued to make an informed decision and to protect the rights of all persons involved," he said.
Marines have repeatedly described the rebels they fought against in Falluja as ruthless fighters who didn't play by the rules. They say the investigation is politically motivated.
"It's all political. This Marine has been under attack for days. It has nothing to do with what he did," said Corporal Keith Hoy, 23.
Rights group Amnesty International said on Monday both sides in the Falluja fighting had broken the rules of war governing the protection of civilians and wounded combatants.
Gunnery Sergeant Christopher Garza, 30, favored an investigation but like other Marines said the Pentagon should weigh its decision carefully.
"He should have captured him. Maybe the insurgent had some valuable information. There may have been mitigating circumstances. Maybe his two buddies died in Falluja," he said.
Sites said: "I have witnessed the Marines behaving as a disciplined and professional force throughout this offensive. In this particular case, it certainly was a confusing situation to say the least."
The U.S. military has been embarrassed by scandals in Iraq, most prominently the Abu Ghraib affair in which at least eight U.S. soldiers have been tried or face courts-martial over the abuse of prisoners at the jail outside Baghdad.
There have also been several cases in which soldiers have been charged with wrongfully killing Iraqis during operations.