Five judges at the Court Martial Appeal Court in London have been urged to free Sergeant Alexander Blackman from jail following the reduction of his murder conviction to diminished responsibility manslaughter.
After hearing mitigation on his behalf on Friday, the judges announced that they will give their decision on Tuesday about what sentence should now be imposed.
There was a huge sigh of disappointment in the packed courtroom from supporters when the announcement was made by Lord Chief Justice Lord Thomas.
Blackman, 42, from Taunton in Somerset, watched the proceedings via video-link from prison.
Jonathan Goldberg QC, told the judges that "at the forefront of our submission is the plea that he should be released today".
He said "the incarceration of almost three-and-a-half years which he has already served is already too much for his crime".
The judges had previously ruled that Blackman was suffering from an "abnormality of mental functioning" at the time of the incident.
When the court overturned the murder conviction, the judges found that the incident was not a "cold-blooded execution" as a court martial had earlier concluded, but the result of a mental illness - an "adjustment disorder".
Blackman was convicted of murder in November 2013 by a court martial in Bulford, Wiltshire, and sentenced to life with a minimum term of 10 years.
That term was later reduced to eight years on appeal because of the combat stress disorder he was suffering from at the time of the killing in Helmand province while serving with Plymouth-based 42 Commando.
The five appeal judges said Blackman had been "an exemplary soldier before his deployment to Afghanistan in March 2011", but had "suffered from quite exceptional stressors" during that deployment.
They found that his ability to "form a rational judgment" was "substantially impaired".
Blackman shot the insurgent, who had been seriously injured in an attack by an Apache helicopter, in the chest at close range with a 9mm pistol before quoting a phrase from Shakespeare as the man convulsed and died in front of him.
He told him: ''There you are. Shuffle off this mortal coil, you c***. It's nothing you wouldn't do to us.''
He then turned to comrades and said: ''Obviously this doesn't go anywhere, fellas. I just broke the Geneva Convention.''
The shooting was captured on a camera mounted on the helmet of another Royal Marine.
During his trial, Blackman, who denied murder and was known at that stage as Marine A, said he believed the victim was already dead and he was taking out his anger on a corpse.
Blackman's wife, Claire, went into the witness box to speak on her husband's behalf on Friday.
Asked by Mr Goldberg what she thought was the greatest punishment for him, she said: "The arrest and conviction were a huge shock, but I think it was the dismissal with disgrace which was the hardest aspect of the whole episode to bear."
After the judges said their ruling would be given next week, Blackman smiled and waved at supporters before the courtroom was cleared to allow Mrs Blackman to speak to him privately.
After the hearing, Mrs Blackman said: "We are obviously disappointed not to have a decision today, but we understand that the judges wish to consider this important matter with great care.
"We will patiently await their ruling."