Footage of Canadian soldiers sporting Kurdish flags on their uniforms in Iraq has raised questions about Canada’s military training mission in the war-torn country.

Canadian military personnel are training Kurdish Peshmerga forces in northern Iraq in their fight against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS).

Footage shot by Canadian news channel CTV in Iraq showed Canadian troops wearing the red, green and white flag of Kurdistan, with a yellow sun at its centre, on one sleeve of their uniforms in late April.

A spokesperson for the Department of National Defence told Al Jazeera the Kurdish flag is being used to ensure troop safety.

"Our members are wearing the flag of the Iraqi Kurdistan Region to enhance cohesion with partner forces and to ensure easy visual identification, which contributes to force protection," Daniel Lebouthillier said in an email.

"Canada remains committed to a unified, stable and secure Iraq."

But critics say the flags - which represent the autonomous Kurdish region of Iraq, under the control of the Kurdistan Regional Government (KRG) - send the wrong message, and may actually run counter to Canada’s stated mission in the country.

"We are supposed to be there supporting Iraq and everyone agrees that strengthening Iraq so that it can take on Islamic State is what is needed," said Peggy Mason, president of the Rideau Institute, an independent foreign policy think-tank in Ottawa.

"I frankly find it quite incomprehensible that Canadian soldiers would be wearing the Kurdish flag."

Canada ended air strikes in Iraq and Syria in mid-February, fulfilling a campaign promise made by Prime Minister Justin Trudeau and his Liberal party, and bolstered its training mission of Kurdish forces in northern Iraq.

Canada is also continuing to assist the international coalition fighting ISIL with air-to-air refuelling and aerial surveillance and reconnaissance.

Thomas Juneau, an assistant professor of public and international relations at the University of Ottawa, said Canadian troops wearing the Kurdish flag “is a pretty marginal issue”.

But he said it raises a larger question about Canada’s short- and long-term goals in Iraq.

READ MORE: Canada to end bombing missions in Iraq and Syria

Canada does not support the prospect of an independent Kurdistan and wants Kurds to reintegrate into the politics of Iraq more generally, Juneau told Al Jazeera, but at the same time it is strengthening the Kurdistan Regional Government (KRG).

"In the short term, it does make strategic sense to support the KRG because they’re one of the best actors on the ground against the Islamic State," Juneau said. "But in the long term it doesn’t make sense."

Still, Juneau said the flag could be strictly operational, as Ottawa has said.

Kurdish forces shot and killed a Canadian soldier in a case of friendly fire in northern Iraq last year, and "as one way to mitigate against the risk of that happening, it’s not a bad idea," Juneau said.

But the flag of Kurdistan is loaded with symbolism, as leaders of the Kurdish national movement first unveiled it in the early 20th century.

"It’s a symbol of Kurdish separatism and therefore the wearers of it would be considered to be associated with it," Mason told Al Jazeera.

"If Canadian soldiers are wearing this flag, then it certainly gives the impression that Canada supports this."