Danny Fitzsimons was sentenced to at least 20 years in prison in 2011 for killing Scot Paul McGuigan and Australian Darren Hoare in Baghdad in August 2009.
All were working for UK security firm G4S, which was operating under the name ArmorGroup in the region.
Tonight's programme, BBC Scotland Investigates: Britain's Private War, claims that a G4S whistleblower sent a series of emails to the company in London, warning them about Fitzsimons's previous convictions and unstable behaviour.
Signing one email: "A concerned member of the public and father", the anonymous worker warns G4S: "I am alarmed that he will shortly be allowed to handle a weapon and be exposed to members of the public. I am speaking out because I feel that people should not be put at risk."
Another email, sent as Fitzsimons was due to start work in Baghdad, says: "Having made you aware of the issues regarding the violent criminal Danny Fitzsimons, it has been noted that you have not taken my advice and still choose to employ him in a position of trust. I have told you that he remains a threat and you have done nothing."
The programme reports that Fitzsimons had worked as a private security contractor before in Iraq, but he had been sacked for punching a client.
In the documentary, the parents of Paul McGuigan call for the company to face criminal charges over the killing. Corinne Boyd-Russell, from Innerleithen, in the Borders, said: "[Fitzsimons] fired the bullets. But the gun was put in his hand by G4S ArmorGroup. They put the gun in that man's hand.
"I want G4S to be charged with corporate manslaughter and be held accountable for what they did."
The parents of Fitzsimons were also shocked to hear about the existence of the emails.
Liz Fitzsimons, from Manchester, said: "And they still took him out there? They [G4S] need to be taken to task for that.
"The people who we feel are responsible, who we hold responsible for putting that gun in Danny's hand, are without a shadow of a doubt G4S."
A G4S spokesman said: "This was a tragic case and our thoughts remain with the families of both Paul McGuigan and Darren Hoare, who were valued and highly respected employees of the company, and who continue to be sadly missed by their families, colleagues and friends alike.
"We confirmed publicly on September 15, 2009, that, in this particular case, although there was evidence that Mr Fitzsimons falsified and apparently withheld material information during the recruitment process, his screening was not completed in line with the company's procedures.
"Our screening processes should have been better implemented in this situation but it is a matter of speculation what, if any, role this may have played in the incident.
"We received two separate medical documents which certified that Mr Fitzsimons was fit to work in Iraq.
"It subsequently came to light that the most recent of those documents was forged – we believe falsified by Mr Fitzsimons.
"Mr Fitzsimons was also found to be mentally fit to stand trial by a court of law before he was found solely responsible for and convicted of the killing of Paul and Darren.
"We have not been shown any formal documentation which proves Mr Fitzsimons had post-traumatic stress disorder.
"We are aware of the allegation over emails but following an internal IT investigation it is clear that no such emails were received by any employee before the incident.
The spokesman continued: "It is not for G4S to comment on the appropriateness of any criminal investigation.
"The company has fully and unconditionally co-operated with enquiries from the police and authorities in both the UK and Iraq at all times."
The documentary will be screened at 9pm tonight on BBC Two Scotland.
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