In a statement today to the inquiry into Pte Kovco's death, Air Chief Marshall Angus Houston says he repeatedly told Dr Nelson shortly after the April 21 shooting that details about exactly what happened to the Victorian soldier were unclear.
He also told the minister several times that a proper investigation was needed and a board of inquiry would be set up to determine how Pte Kovco was shot in his Baghdad barracks.
Despite the warnings from his defence chief, Dr Nelson told the media the day after Pte Kovco died that the soldier was shot while "maintaining" his 9mm Browning pistol.
However, five days later he was forced to make an embarrassing turnaround, changing his story to say the 25-year-old soldier was shot after accidentally knocking his gun.
In his own statement to the inquiry yesterday, Dr Nelson said he based his public statements on information from his defence chief and the Chief of Army, Lieutenant-General Peter Leahy.
But Air Chief Marshal Houston insists he told Dr Nelson several times the circumstances surrounding the shooting were unclear.
Ministerial submissions and background notes on the shooting provided to Dr Nelson by defence, and tendered to the inquiry today, also offer no theories about how the shooting happened.
However, some of those documents specifically warned the minister: "Speculation about what Pte Kovco was doing with the weapon is unhelpful at this time."
On April 24, Air Vice Marshal Houston told Dr Nelson a quick assessment of the shooting had been carried out by an army official in Baghdad. The defence chief said he was careful not to deviate from information in the quick assessment report, which said while it appeared the shooting was accidental it was unclear who fired the pistol.
It recommended a formal investigation by military police.
The inquiry has been adjourned until September 18, when closing submissions will be heard.
The three-man board of inquiry is expected to then take up to eight weeks to prepare a report for Air Chief Marshall Houston.