CBS News on Wednesday said it had learned that military investigators had concluded insufficient evidence existed to formally charge the marine with murder.
However, US Marine Corps spokesman Captain Dan McSweeney said he had been informed by the Navy Criminal Investigative Services which is investigating the killing that "the case is still very much open".
The shooting on 13 November occurred during a search of a mosque.
The killing - filmed by an embedded cameraman working for the NBC network - sparked global outrage and was described by the International Committee of the Red Cross as a demonstration of "utter contempt for humanity".
In the incident, a soldier raised his rifle and shot point blank at an apparently unarmed, wounded Iraqi who was slumped against one of the mosque walls.
Although the Iraqis were found to be unarmed, investigators said the marine believed the man he shot was trying to reach for a weapon.
The rifleman was withdrawn from combat pending the results of the investigation, but the graphic footage enraged many.
The raid on Falluja was part of an attempt to regain the city before Iraq's January elections.
In a separate development, a London-newspaper has reported that as many as 11 more British soldiers could face a court martial over the case of a fatal beating of an Iraqi civilian and other instances of abuse.
Without citing sources, The Times said army lawyers were considering bringing charges against 11 more soldiers linked to abuse cases that had led to deaths of Iraqis.
The report comes a day after two British soldiers were found guilty of mistreating Iraqis in the city of Basra. A third had already pleaded guilty to one charge of assault.
The defence ministry in London confirmed that army prosecutors were considering nine cases, three of them involving alleged abuse.
Seven soldiers from the 3rd Parachute Regiment have already been charged with murder and violent disorder, and face a court martial over the death of an Iraqi civilian in southern Iraq in May 2003.
The 11 new cases could be linked to that death, as well as two other alleged instances of abuse in Iraq that led to deaths, The Times said.