Rochdale-born Danny Fitzsimons, 29, is accused of killing Paul McGuigan, 37, from Tameside, and Australian Darren Hoare, 37, in August.
Heywood and Middleton MP Jim Dobbin is supporting the family's appeal to bring Mr Fitzsimons home and is putting pressure on the British government to intervene.
He is due to appear in court in Baghdad next month after his trial was adjourned on Sunday. All three men worked for British security firm ArmorGroup.
Mr Fitzsimons, who is said to be suffering from post traumatic stress disorder, has said he cannot remember anything of the incident. If convicted he could face the death penalty under Iraqi law and would be the first Westerner to face a murder trial in the country since a deal giving foreign workers immunity was lifted.
Mr McGuigan and Mr Hoare were allegedly shot after a vodka-fuelled row at 4am in the firm's compound near the Republican Palace in Baghdad.
Mr Fitzsimons' step-mum Liz, of Whitworth, wants him to be brought home and said: "The incident was not as cut and dried as it seems, there needs to be a proper investigation."
Solicitor John Tipple believes security breaches that have taken place since his arrest are proof Mr Fitzsimonds cannot receive a fair trial in Iraq. He said: "We don't consider the Iraqi regime is in a state for a fair trial. Sunday's hearing was cancelled because of the latest bombing. There have been several breaches of security. Only last week a huge car bomb went off during the security checks.
War-torn
"There is discontent right the way through the country, it is war-torn and dysfunctional."
Mr Dobbin said: "The aim is to ensure he gets a fair trial. He is suffering post traumatic stress, brought on by a number of years in Afghanistan.
"He has been left with mental health problems and has had difficulties in the past with other issues. There is a possibility of capital punishment if he is found guilty and my hope is the government will intervene. We want to get him back as soon as possible."
Former soldier Mr McGuigan lived with fiancée Nicci Prestage in Tameside and the couple planned to wed next year. She gave birth to their first child last month.
Tweet
MancLadUK, Manchester (18/11/2009 at 09:56)
If we were to try to bring this person home to face trial here we are robbing the Iraqi victim of his justice, we are insulting a country we are allegedly trying to help to restore a justice system and we're executing extreme double standards in the process.
If an Iraqi national was accused of a crime in the UK would you be happy for them to be flown back to Iraq to face trial instead of facing trial here where the offence was committed? Not a chance!
To allow this man to come here for trial is something I'd be ashamed of as a nation. It would show to the rest of the world that we as a country see ourselves as above other countries, above their laws and able to do as we please. He should stay in Iraq for his trial.
I would hope the MP sees sense and allows the people of Iraq to see the UK as a country playing by the rules and not simple pushing them around, making it up as we go along and simply not respecting their laws.
Any petitions or actions to bring this man home should be counter actioned by the same to keep him there. Let the country where he is alleged to have committed the offence be allowed to try him for it as we ourselves would want in this country!