The 25 year old was the first Australian soldier to be killed while serving in Iraq.
A formal board of inquiry would be established into the death of Private Kovco as soon possible and would last four to six months, Dr Nelson said today.
The board will be headed by Group Captain Warren Cook, a former NSW coroner, and will comprise of former Queensland police commissioner Jim O'Sullivan and Colonel Michael Charles.
The inquiry would be held at Sydney's Victoria Army Barracks, Dr Nelson said.
"Australians can be assured that an open and thorough process is about to commence that will get to the bottom of this," he told reporters.
Meanwhile, Dr Nelson has stood by his department's response to the incident, saying he was acting on the best advice given to him by defence officials at the time.
"As I have said since this tragic event has occurred, there is no evidence at this stage to suggest that it was anything other than a tragic accident," he said.
Body reunited with family
Private Kovco's body is back on home soil, after being greeted with a full military guard of honour at Sydney airport.
The return of his body had been delayed by a bungle which resulted in the wrong body dispatched from a mortuary in Kuwait.
His body was supposed to have been flown to Melbourne on Thursday.
But the remains of a Bosnian civilian contractor who had been working in Iraq arrived at the airport instead.
An airplane carrying Private Kovco’s body touched down in Sydney at about 7.30am AEST.
Guard of honour
In full parade dress and wearing black arm bands, about 300 officers from Private Kovco’s regiment of the 3rd Battalion Royal Australian Regiment at Holsworthy formed a guard of honour from the doorway of the aircraft.
They saluted the silver casket as it passed.
Eight military pallbearers carried the coffin which was draped in an Australian flag with a wreath of red flowers on top.
A lone piper played a lament while light rain fell as the silver coffin made its way across the tarmac to the family including his widow Shelley.
Mrs Kovco and the private's parents laid their hands on the coffin, which was draped in the Australian flag and had his beret and a wreath of flowers on top.
Airport security and other staff came to a standstill as the procession passed.
The chief of the defence force Air Chief Marshal Angus Houston, Defence Minister Brendan Nelson and opposition defence spokesman Robert McClelland were also paid their respects.
After the viewing on the tarmac by family and friends, Private Kovco’s body was handed over to the New South Wales Coroner.
The coffin was loaded into a black hearse and wiping tears from her eyes, his widow got into the vehicle to accompany it to Glebe Morgue where there will be a coronial inquest.
Accidental shooting
Private Kovco died when he was accidentally shot with his own Browning 9mm pistol last Friday night.
Last weekend, Dr Nelson said it was thought that the experienced marksman shot himself while cleaning his gun.
But Dr Nelson now says that is not the case.
NSW police and the state coroner will investigate the shooting, amid claims from his family of a cover-up over his death.
A funeral is planned in his home town in Briagolong, 270km east of Melbourne, on Tuesday.