A former head of the armed forces has challenged senior military figures who have called for clemency over the Royal Marine found guilty of killing a Taliban prisoner in Afghanistan. Lord Guthrie told the Observer on Saturday that "murder is murder" and the soldier should be punished severely.

The first chief of the defence staff under new Labour said that British soldiers, even when operating under the pressures of war, should never be considered above the law.

He added: "My view is that the military should observe the highest standards, and if some crime is committed, like everybody else they should pay the price. I don't know whether there were any mitigating circumstances, but murder is murder."

The serviceman, known only as Marine A, was convicted on Friday, at the end of a two-week court martial, of murdering the wounded prisoner in Helmand province two years ago.

Major General Julian Thompson, one of the Royal Marines' most distinguished officers, had earlier said that the unique psychological pressures of war should be taken into account when assessing such cases.

"The more times you do tours in that filthy war the more pressure there is on you," Thompson said. "I'm not going to stand around bad-mouthing him. I won't condemn him. It is like a member of the family who has broken the law – you don't reject them, but you support them."

Marine A faces a life sentence.

However, Thompson, who led 3 Commando Brigade during the Falklands war, said life imprisonment would be too harsh and suggested that a five-year term was more appropriate for a crime committed in the pressure-cooker environment of combat.

Reports have suggested a number of deaths suffered by Marine A's unit in the months before the murder could have provided a motive for the crime.

"The whole story is very regrettable. The court behaved as it should and reached the correct verdict," said Guthrie, who was chief of the defence staff between 1997 and 2001.

David Cameron also joined the debate on Saturday by backing the Royal Marines after a military court convicted the 39-year-old marine of the "battlefield execution" of an insurgent. The prime minister said the guilty verdict should not "besmirch" the marines' proud history. The incident "in no way represents the incredible spirit, courage and history of the Royal Marines", he said.

It is the first time that a British marine has been convicted of a war crime during the 12-year conflict. Two others, known only as Marines B and C, present during the incident, were acquitted of murder.

Marine A was convicted after footage emerged of him shooting the insurgent at close range in the centre of his chest. As the man convulsed on the ground, Marine A told him: "There you are. Shuffle off this mortal coil, you cunt. It's nothing you wouldn't do to us."

He then turned to his colleagues and said: "Obviously this doesn't go anywhere, fellas. I just broke the Geneva convention."

The court heard the marines were on patrol on 15 September 2011 when they found the insurgent lying gravely injured in a field after an attack by an Apache helicopter. Superiors were informed the man had died in the gunship attack, in which 139 30mm anti-tank rounds were fired at him. However, footage of the murder – taken from a camera on the helmet of Marine B – was discovered on a laptop by military police investigating unrelated matters. The court refused to release the film for fear of encouraging reprisals. Only the audio of the murder and a transcript of the video were made publicly available.

Marine A told the court martial he thought the insurgent was already dead when he shot him, and said he did so out of anger, calling it "stupid, lack of self-control, momentary lapse in my judgment". Marine B admitted members of the patrol had lied during interviews to protect their comrade. Marine A was remanded in custody to be sentenced on 6 December. Marines B and C were freed and have returned to normal duties. The issue of identifying Marines A, B and C – as well as two others, named only as Marines D and E, who were also on the patrol – will be determined at an appeal hearing after the judge ruled they should be identified.