The man was one of five wounded and left in the mosque after US marines fought their way through the area.
A second group of marines entered the mosque on Saturday after reports that fighters opposed to the US presence in Iraq had moved back into it.
Footage from the NBC television crew showed the five still in the mosque. Several appeared to be already close to death, NBC correspondent Kevin Sites said.
He said a marine noticed one prisoner was still breathing. "The marine then raises his rifle and fires into the man's head. The pictures are too graphic for us to broadcast," Sites said.
Rights group Amnesty International said on Monday that both sides in the Falluja fighting had broken the rules governing the rules of war protecting civilians and wounded combatants.
Top UN human rights official Louise Arbour called on Tuesday for an investigation of alleged abuses in Falluja such as disproportionate use of force and the targeting of civilians.
Top level accountability
In an interview with Aljazeera, US marine spokesperson 1st Lieutenant Lyle Gilbert responded to the killing of the wounded man in the Falluja mosque.
"I was not there and have no more information. The pictures were shown on TV but they did not reveal the circumstance that preceded the incidence. We will know after the investigation finishes.
"We the US forces abide by the combat laws and consider ourselves at the top level of accountability."
In response to reports by Falluja residents that US forces had executed injured Iraqis and dragged them behind US tanks Gilbert said: "I will not talk about this issue. The US, together with Iraqi forces confronted the terrorists in Falluja.
The forces are there to clean the city from rebels and terrorists, regain stability and security in Iraq and to hold elections so the Iraqi children can play in playgrounds," he said.
Did nothing wrong
Marines interviewed in Falluja on Tuesday said they did not see the shooting as a scandal, rather the act of a comrade who faced intense pressure during the assault on the city.
"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 Falluja offensive sparked
more unrest in Iraq
Meanwhile violence around Falluja continued as four US military boats were attacked and a number of soldiers aboard were wounded after an operation by armed men in the Nassaf district, west of Falluja city, Aljazeera has learned.
Earlier on Tuesday a marine was killed in a car-bomb attack in the south of the city, a marine officer said.
At least 39 US soldiers have been killed since the start of the Falluja offensive eight days ago and more than 250 injured according to the US military.
Crisis played down
Iraq's US-backed interim government has dismissed reports that civilians in Falluja were desperately short of supplies and lacked adequate medical care. Most civilians were reported to have fled the city of 300,000 before the start of the offensive a week ago.
"The Iraqi government strongly rejects suggestions from some sources that there are shortages of supplies in Falluja," a statement from interim Prime Minister Iyad Allawi's office said.
A marine was killed by a car
bomb in the south of Falluja
An Iraqi health ministry team had visited the city and Falluja hospital and found no shortages, the statement said, adding: "They have confirmed that they found no citizens in need of food or water. It is now clear there are very few citizens in Falluja. Most have already fled from the terrorists."
But the acting manager of Falluja hospital, Salah Isawi, told Aljazeera that the humanitarian situation in the city was still "a disaster".
"We expect there is a disaster in the city. A woman called us pleading [with] us; she said that she is alone with no water, electricity or food and she was scared.
"I plead with the Iraqi ministry of health to pressure the government and US troops to allow relief teams and medical staff to enter the city," he said.
Surge in unrest
The Falluja offensive has sparked a surge in unrest in other areas. In Baquba, northeast of Baghdad, five policemen and 26 fighters were killed in fighting on Monday.
Renewed clashes erupted in the town on Tuesday, residents said.
US troops were also engaging fighters on Tuesday in the northern oil refining town of Baiji, witnesses said.
They said fighters had taken to the streets and were waging gun battles with American and Iraqi forces.