Prime Minister Ayad Allawi (search) is "very concerned" about the fatal shooting by a U.S. Marine of a wounded and apparently unarmed man in a Fallujah mosque, his office said Wednesday.

The U.S. military said its investigation would look into whether other wounded men in the mosque were similarly killed.

American and Iraqi authorities have been trying to stem outrage over the shootings among Iraqis, particularly the Sunni Arab minority, and Arabs across the region.

U.S. Ambassador John Negroponte (search) expressed regret over the shooting but said Wednesday it should not undermine U.S. efforts to remove guerrillas from the city.

The U.S. military said Tuesday it was investigating after pool video footage by NBC showed a Marine shooting a wounded man lying in a Fallujah mosque during an operation Saturday of the 3rd Battalion, 1st Marine Regiment (search).

Military investigators also are looking into whether more than one wounded insurgent was shot in the mosque, said Maj. Francis Piccoli, a spokesman for the 1st Marine Expeditionary Force (search).

Two other men visible on the NBC video appear to be suffering from what the network described as fresh and fatal gunshot wounds.

"The prime minister is very concerned by allegations of an illegal killing by multinational forces in Fallujah," the statement from Allawi's office said. "He has discussed the matter with the commander of the multinational force in Iraq," Gen. George Casey (search).

"Gen. Casey has assured the prime minister that an urgent inquiry is under way, and that he will share its findings with the Iraqi government in full and with complete transparency," the statement added. "Unlike others, the prime minister will await the outcome of the investigation before commenting any further on this incident."

Negroponte said "no one can be happy" about the incident, "but the important point is that the individual in question will be dealt with."

"The matter is being looked into and whatever measures are necessary under our system of military justice I know will be taken," he said.

"But I don't think that [the incident] in any way is a reflection on the quality and caliber of absolutely fine young servicemen and women we have serving here in Iraq," he said during his first visit to Sadr City (search), a large Shiite Muslim district of Baghdad.

The shooting occurred when a Marine unit entered the mosque and found five men wounded in fighting at the site the day before, when another Marine unit clashed with gunmen apparently using the mosque to fire from, according to NBC's Kevin Sites, the pool correspondent who took the footage.

In the video, as the cameraman moved into the mosque, a Marine can be heard shouting obscenities in the background, yelling that one of the men was only pretending to be dead. The Marine then raises his rifle toward an Iraqi lying on the floor of the mosque and shoots the man.

Two other men are seen slumped by a wall. Sites' account said the men, who were hurt in the previous day's attack, had been shot again by the Marines on Saturday.

Earlier in the footage, as the Marine unit that Sites was accompanying approached the mosque, gunfire can be heard from inside. Marines who were already in the mosque emerge, and a lieutenant in the approaching unit asks if there were insurgents inside and if the Marines had shot any of them. An exiting Marine can be heard responding affirmatively. The lieutenant then asks if they were armed, and the Marine shrugs.

Negroponte also said the fight for Fallujah — for months the main insurgent bastion — was important for the U.S. mission in Iraq, even though guerrilla leaders remain on the loose, resistance has not been crushed and attacks have increased throughout central Iraq.

"I think the liberation of Fallujah is extremely important," he said. "Former regime elements and foreign fighters have been deprived of a sanctuary and a base they were using as a platform for conducting terrorist activities throughout the rest of the country, especially here in Baghdad."

The purging of militants from the insurgent stronghold west of Baghdad also "sets the stage for the entry of humanitarian assistance and resumption of economic activities."

"We have over $100 million worth of reconstruction projects and that all awaits the completion of liberation of the city," Negroponte said. "Hopefully, Fallujah will return to a much better life."