Mr Howard said because the 25-year-old father of two died on active service, the government had to accept responsibility.
"I, in particular, accept full responsibility," Mr Howard said. "It was our decision to commit military forces to Iraq and I am very conscious of that."
Private Kovco, died from a gunshot wound in the Iraqi capital Baghdad last Friday. There are varying reports of the circumstances of Private Kovco's death which has become the subject of an inquiry.
The prime minister’s statement came as the body of Australian soldier finally begun the journey home after a mix-up saw another body arrive in Melbourne early Thursday.
Call for patience
Mr Howard urged patience and an end to speculation as the defence department begins investigations into how Private Kovco was fatally shot and how his body was mistakenly left behind in Kuwait.
"We will find out what happened, just as there will be a full inquiry into the circumstances of Private Kovco's death,” he said.
“I don't know the circumstances and it would be in everybody's interests for there to be no further comment on what might have happened until the inquiry brings down its findings," Mr Howard told Southern Cross Radio.
He has said the soldier’s body was due to arrive back in Australia some time between midnight and 1AM (AEST) Saturday.
The 25-year-old soldier was part of the Australian security detachment in the Iraqi capital.
Distraught family
The family of the deceased soldier has lashed out at the defence department and the federal government over the mix-up and accused the military of covering up the cause of his death.
On Thursday Defence Minister Brendan Nelson revealed that Private Kovco was not cleaning his pistol when he was killed, as he had previously said, and that the weapon accidentally discharged.
The family is angry that Mr Nelson has changed the government's original story.
Private Kovco's angry widow Shelley forcefully expressed her unhappiness to the Prime Minister when she spoke to him by phone at The Lodge shortly after the mix-up was revealed.
Mr Howard said he felt desperately sorry for Mrs Kovco, who declined an offer to be flown to Kuwait aboard the prime minister's jet.
Review
The Australian Defence Force has said it drew up a plan to better handle the repatriation of soldiers who die overseas, but it was rejected by state coroners.
The plan was based on the successful repatriation of nine bodies after the Sea King crash in Indonesia.
But state and territory coroners, who have a long history of working with the military on inquests and investigations, said the plan would have compromised their independence.