The US military promised an investigation into the shooting amid allegations that marines shot three other wounded insurgents execution-style.
A marine was televised killing the man after noticing that he was still breathing. In footage filmed by an embedded television reporter for NBC, one soldier was caught on camera saying: "He's fucking faking he's dead."
"The marine then raises his rifle and fires into the man's head," said the NBC reporter, Kevin Sites. The marine was heard immediately afterwards saying: "He's dead now."
The protection of wounded combatants is a basic tenet of the Geneva conventions which govern the rules of war. Amnesty International has accused both sides of breaking these rules.
Louise Arbour, the UN high commissioner for human rights, said yesterday all those responsible for violations should be brought to justice.
All violations of international humanitarian and human rights law had to be investigated, she said, including "the deliberate targeting of civilians, indiscriminate and disproportionate attacks [and] the killing of injured persons."
Fellow marines said yesterday they saw the shooting as the act of a comrade who faced intense pressure. "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," Lance Corporal Christopher Hanson told Reuters.
Sergeant Nicholas Graham said: "You can't trust these people... He did nothing wrong."
The footage provoked anger in the Arab world where some al-Jazeera viewers compared it to the Abu Ghraib torture pictures.
Most British broadcasters decided not to show the moment of death, although Channel Five showed the whole sequence in its 7pm bulletin, followed by a discussion of the pictures.
· The US military has charged 2nd Lieutenant Erick Anderson with premeditated murder for his part in the shooting of an injured Iraqi man in Baghdad in August, officials said yesterday.