Australian Prime Minister John Howard vowed there would be no cover-up over the death of Private Jake Kovco, but he urged patience so an inquiry can reach the truth of what happened.
But he said a full explanation could be weeks or months away.
Private Kovco's widow and family have expressed anger not only about the bungle but also over confusion surrounding the exact circumstances of his shooting death in Baghdad on Friday.
New South Wales Coroner John Abernathy said he expects to assume jurisdiction for Private Kovco's body when it arrives in Sydney, and the NSW police will take change of the investigation into his death.
The Defence Department said a Guard and Bearer Party of soldiers will receive the body and carry it to a ceremony with family members, with a funeral expected to be held in his home town of Briagolong, Victoria, early next week.
Mr Howard said it is not possible to give Private Kovco's mother, who has already alleged an army cover-up, a complete explanation without a proper formal legal inquiry.
"The only answer I can give is that I do not know precisely what happened. I wasn't there and we do need a proper investigation," he told Southern Cross radio.
"This will not be covered up. It can't be covered up because there's going to be a proper investigation."
Mr Howard said he doesn't know the circumstances of Private Kovco's death and it will be in everybody's interests for there to be no further comment on what might have happened until the inquiry reports.
Private Kovco, 25, a member of the Australian army security detachment in Baghdad, died when he was accidentally shot with his own Browning 9mm pistol.
Exactly how that happened hasn't been explained.
Compounding the tragedy, Private Kovco's remains were mistakenly left behind in Kuwait and another body was flown to Melbourne.
Private contractors have been blamed for the mishap.
Mr Howard suggested incomplete early accounts might have contributed to Defence Minister Brendan Nelson's differing explanations of how Private Kovco died.
Dr Nelson initially said the soldier was handling and maintaining his gun when it discharged. He subsequently said he was not handling the gun at the time - raising questions from family members about what really happened.
Two fellow soldiers were in the room at the time of the shooting, although officials said neither witnessed the incident.