Sun McKay, 39, is now believed to be under armed guard in the Iraqi capital, after fellow Australian contractor Chris Betts was found dead in his room on Thursday from a gunshot to the head.
Colleagues have said both men had been drinking in their accommodation block before the shooting about 2:30am.
A former embassy guard who worked with both men at the private security firm Unity Resources Group told the ABC he and his colleagues had long been concerned about Mr McKay’s behaviour.
“In 2010 he was reported to management after making threats to shoot people who upset him,” the former private security guard said speaking on the condition of anonymity.
Another former Australian soldier Murdoch White began an investigation into the alleged threats, but it was later dropped after Mr McKay’s colleagues decided not to lodge formal complaints against him.
In 2009 Mr McKay was detained for several months in Dubai after an altercation with a policeman at the airport.
During his detention he told the Seven Network he felt “incredibly lonely” and “incredibly homesick”.
The ABC understands federal police have now begun searching Mr McKay’s room in the Iraqi capital as they continue their investigations.
Last weekend Mr McKay’s cousin John McKay appealed for the public to reserve its judgement on his relative.
“I ask people to not judge Sun at all until the full true facts can come out,” he told reporters in Adelaide on Saturday.
“There is no doubt in my mind that what he has said is what happened.”
John McKay said the fact his cousin was part of Prime Minister Malcolm Turnbull’s security detail during his visit to Iraq in January was proof of his good character.
“He wouldn’t have been put in the position to be in that car with Mr Turnbull if they didn’t think he was safe and secure and clear headed,” Mr McKay said.