The Canadian government and Kurdish officials are publicly at odds over a Canadian soldier's death in a friendly fire incident in Iraq.

The death of Sgt. Andrew Joseph Doiron on Friday marked Canada's first casualty as part of the U.S.-led coalition's war on the extremist Islamic State in Iraq and Syria group.

Kurdish officials said Sunday that Doiron was killed after he and other Canadian soldiers showed up to the front line unannounced to call in airstrikes.

"They went to the front line to direct airstrikes because the area was attacked by ISIS the day before," Hezhar Ismail, director of co-ordination and relations for the peshmerga, the Kurdish fighters, told The Associated Press.

Another peshmerga spokesman, Halgurd Hekmat, said the group of Canadians had been in the village of Bashiq, in Iraq's Nineveh province near the militant-held city of Mosul.

"When they returned, the peshmerga asked them to identify themselves," Hekmat told the AP. "They answered in Arabic, that's when peshmerga started shooting. It was their fault."

We would ask that the Kurdish authorities ... co-operate with our inquiries, so that we can get to the bottom of this terribly tragic accident and ensure that it does not happen again. - Defence Minister Jason Kenney

But a high-level Canadian government source disputed that account, telling CBC News that Doiron and three fellow soldiers were a couple hundred metres from the front line and had pre-arranged a rendezvous with Kurdish troops that went awry.

The Canadian team had been at the location earlier in the day "to co-ordinate events to take place later" and had arranged a time to return that night, with pre-determined signals to identify themselves to the Kurdish troops, according to the source, who spoke on condition of anonymity. "Special forces don't freelance," he said, disputing the Kurdish account that they showed up unannoucned. He added that the soldiers had operated using this system before.

The Canadians arrived for the rendezvous and were acknowledged by two separate groups of peshmerga fighters without incident, the source said. A third peshmerga group, however, engaged them by opening fire.

Separately, Defence Minister Jason Kenney was also adamant that the Canadian soldiers were well behind the front lines when Doiron was killed. "They were approaching a Kurdish observation post behind the forward operating line," he said in an interview with CBC News. "They clearly identified themselves, and our understanding is that they were given permission to proceed toward the observation post....

"One of the Kurdish militiamen began to shoot at the four Canadian soldiers and others joined. So this appears to have been a tragic case case of mistaken identity."

Minister of national defence says Kurdish accounts of the death of Sgt. Andrew Joseph Doiron do not correspond to reports received from Canadian forces in Iraq 9:37

CBC News has also learned that the three surviving soldiers suffered injuries that are considered non-fatal, and one of them has been evacuated to Germany for medical treatment.

Kenney later tweeted that he thanked U.S. Secretary of Defence Ashton Carter "for the excellent medical support offered to our soldiers by U.S. military" following the incident.

The Canadian military also denied that the group was in the area to direct airstrikes.

"I can confirm it's a big no. They were not there to conduct airstrikes," said Daniel Lebouthillier, a spokesman for the Canadian military.

Kenney told CBC News that the Canadian government is launching two investigations into the incident.

"We would ask that the Kurdish authorities — rather than speculating about this — co-operate with our inquiries, so that we can get to the bottom of this terribly tragic accident and ensure that it does not happen again."

Family asks for privacy

Canada's military on Saturday announced the death of Doiron, a soldier in the Canadian Special Operations Regiment based at Garrison Petawawa, Ont. .

The flag at the entrance to Garrison Petawawa, Ont., is seen flying at half mast on Sunday in honour of the death of Sgt. Andrew Joseph Doiron. (Kamil Karamali/CBC)

Doiron's family released a brief statement Sunday evening asking for privacy and time to grieve.

"Our son gave all, and through his loss, we gave all," it read. "We've lost our beloved son."

Canada sent 69 special forces soldiers to assist Kurdish peshmerga fighters in what the government calls an advising and assisting role. They were sent to help train Kurdish fighters last September in a mission that was billed as noncombat with the elite troops working far behind the front lines.

Canadian soldiers have been helping the Kurdish fighters by directing coalition airstrikes against ISIS fighters, a role generally considered risky because it means they are close to the battle against the militants. The fact that Canadian special forces have been involved so close to the front lines has stirred controversy in the country, but Kenney said the rules of engagement will remain the same.

Doiron's body may be flown back Tuesday

The Canadians' efforts complement those of the United States, which has conducted the vast majority of the airstrikes against the ISIS group. But in their new role, the Canadians are performing a task in targeting airstrikes that so far the U.S. has been unwilling to do. Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, has repeatedly said the U.S. would consider directing attacks from the ground but that it has not yet done so.

Defence Minister Jason Kenney acknowledged the death of Canadian soldier Sgt. Andrew Doiron in Iraq was "a case of mistaken identity." (Fred Chartrand/Canadian Press)

A Canadian military official said Doiron's body won't be flown back to Canada until Tuesday at the earliest and there will be a repatriation ceremony. The official spoke on condition of anonymity as he was not authorized to comment publicly. Kurdish officials, speaking on condition of anonymity, had said earlier that the body would be flown back Sunday following a military ceremony at Irbil International Airport.

ISIS currently holds a third of Iraq and Syria. The U.S.-led coalition began airstrikes targeting the extremists in August.

So far, four other troops have been killed as part of the coalition, not counting Iraqi forces. They include a U.S. Marine presumed lost at sea in October, a Marine killed in a noncombat incident in Baghdad in October, a U.S. Air Force pilot killed in December when his jet crashed in Jordan and a captive Jordanian pilot burned to death in a cage by ISIS.