Sergeant Colin Maclachlan said the motive of soldiers was "entirely humane" when they allegedly dead "two or three" fatally injured enemy combatants during the 2003 invasion.
The 42-year-old, who appeared in Channel 4 programme SAS: Who Dares Wins, said the injured soldiers were screaming in agony and "pleading for us to do it".
Killing mortally wounded enemy soldiers on the battlefield to end their suffering out of mercy is illegal under UK military law and against standards laid down by the Geneva Conventions.
However Mr Maclachlan, from Edinburgh, told the Mail on Sunday that the case showed the "harsh reality of combat" with ordinary servicemen who are put in positions of "extraordinary" decision-making.
He said: "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."
The attack on three Iraqi army vehicles near the Syrian border in March 2003 features in a new book, SAS Who Dares Wins: Leadership Secrets From The Special Forces, to which Mr Maclachlan has contributed a chapter entitled "Handling The Dirty Work".
The Ministry of Defence (MoD) has procedures for considering such manuscripts submitted for publication and reportedly launched a probe into possible crimes after receiving an advanced copy.
According to the Mail on Sunday, Mr Maclachlan was informed of an investigation by military police via email from MoD officials last week.
An MoD spokeswoman said they were unable to comment on the reported inquiry at this time.
Read More
They added: "Our Armed Forces will continue to be held to the very highest standards. Credible allegations of criminal behaviour will always be investigated properly."
Mr Maclachlan subsequently said that he did not carry out mercy killings.
He told The Sun: "If anywhere in that book says there were three wounded guys and I killed them, all that is absolute nonsense."
