Sergeant Colin Maclachlan, 42 - who starred in the Channel 4 series Who Dares Wins - is being investigated by the Ministry of Defence.
He admitted in a new book to shooting dead ‘two or three’ mortally wounded Iraqi troops during a 2003 battle.
Mr Maclachlan said the killings of ‘horrifically wounded’ Iraqis had been an act of mercy and he is reportedly shocked that he is under investigation.
Executing badly wounded enemy troops on the battlefield is illegal under UK military law.
Mr Maclachlan is reported as saying: “Our motives were entirely humane. I’ll happily go to court, I’ll happily go to jail, if you think I’ve done wrong.
“But people should put themselves in my position first. Walk around in my boots, then judge me.”
Detectives became aware of the killings after the MoD was given an advanced manuscript of Mr Maclachlan’s book SAS Who Dares Wins: Leadership Secrets From The Special Forces.
An MoD spokesman said: “Credible allegations of criminal behaviour will always be investigated properly.”