General Sir Nick Houghton said the murder in 2011 in Helmand province was a “heinous crime” and service personnel were not above the law.
His comments came after others, including a retired commander, appealed for leniency in the sentencing of the serviceman – known only as Marine A – who is facing a mandatory life sentence after being convicted at a court martial last week.
A minimum term will be set at a sentencing hearing on 6 December.
At the weekend Major General Julian Thompson, who led 3 Commando Brigade during the Falklands War, said the shooting of the insurgent was “totally wrong, totally unforgiveable”.
But he said it was not known what pressure the serviceman might have been under in the past and some sort of clemency should be exercised.
However, when questioned about the case during the BBC’s Andrew Marr Show, Gen Houghton said it would be wrong for leniency to be requested. He said: “My position on this is that no serviceman or woman is above the law.
“They are not above the law of the country, international law or the law of armed conflict.
“This was a heinous crime. Judicial process has found this individual guilty and it would be quite wrong for the armed forces to adopt some special pleading, some sort of exemption.”
Gen Houghton said he accepted that the marine’s crime, committed under the extreme stress of a conflict situation, was not the same as if it had happened on the streets of a city in the UK.
But he added: “If we try to put ourselves beyond the law, then we start to erode the position where we have a moral ascendancy over those who are our enemies. That is the wrong thing to do.”
Gen Houghton said those who were in authority over the armed forces should not request any form of leniency. “I think it is dangerous to do so,” he said.
The court martial, sitting at the Military Court Centre in Bulford, Wiltshire, saw evidence from a helmet-mounted camera belonging to a marine which captured the insurgent’s death.
The video footage was discovered a year after the event by military police investigating an unrelated matter.
Two of the convicted commando’s comrades, known as Marines B and C, were acquitted of murder.
Prosecutor David Perry told the court the murder “amounted to an execution”. Marine A told the trial his action was “stupid, lack of self-control, momentary lapse in my judgment”.