Iraqi Shia militias, which have borne the brunt of the fighting on the ground against the Sunni jihadists of ISIS in central and western Iraq, say they don't want the coalition’s assistance.
Some groups are refusing to continue fighting and one has even threatened to shoot down coalition aircraft.
The confrontation comes as an Iraqi offensive to retake the ISIS-held city of Tikrit has stalled.
Tikrit is a Sunni-majority town of roughly 250,000 inhabitants about 140 kilometres north of Baghdad, and the birthplace of Saddam Hussein.
An Iraqi government offensive began a month ago to recapture Tikrit. Less than 20 per cent of the approximately 24,000 Iraqi government forces engaged in the fighting are from the regular Iraqi army.
The rest belong to Shia militias known as the popular mobilization committees. Those militias are the ones objecting to coalition airstrikes.
The Shia militias are mostly close to Iran and in many cases are led by Iranian military advisers. The operation to retake Tikrit was supervised by the commander of the Iranian Quds Force (an elite unit of the Revolutionary Guards), Gen. Qassem Suleimani.
The U.S. has poor relations with the militia groups, many of whom once battled the American occupation of Iraq.
U.S. officials have also said they worry that Shia militias will retaliate against Sunni civilians in areas formerly held by ISIS, setting back efforts to reunite the country and heal the wounds of the sectarian civil war that followed the U.S. invasion in 2003.
The Harper government has also seemed uncomfortable at times with Iranian involvement in the campaign against ISIS.
"We don't align with the Iranians," Foreign Minister Rob Nicholson said during a press conference Friday with his U.K. counterpart, Philip Hammond, before quickly changing the subject.
Partly because of the involvement of Iranian forces, and partly because of the presence of Shia militias, the U.S.-led coalition did not launch airstrikes in support of the Tikrit operation.
The Shia militias insisted they could do the job without Western help, and much of the city has been cleared of ISIS fighters. But the ISIS jihadis remain dug into one part of the city that has proved difficult to clear.
On Wednesday, the Iraqi government turned to the U.S.-led coalition, of which Canada is part, to use its warplanes to dislodge ISIS from its redoubts.
But that decision has led some of the most important Shia militia groups to pull out of the fighting.
Canadian defence officials say Canadian planes have not yet been involved in the coalition raids on Tikrit, but CF-18s have frequently bombed targets in the same province of Iraq and routinely fly over the city to hit targets in the Mosul and Kirkuk areas.
Who will take Mosul?
The renewed tension between the Western coalition conducting airstrikes and the forces doing much of the fighting on the ground raises questions about a much bigger offensive planned for later in the spring.
Iraqi forces are supposed to launch an offensive to liberate Mosul by early summer. Mosul is Iraq’s third city and a stronghold of ISIS.
Memories of the grinding battle by U.S. marines to retake Fallujah from insurgents in 2004 must be of concern to coalition war planners. Coalition forces suffered a total of 107 killed and 613 wounded during six weeks of house-to-house combat, and most of the buildings in the city were destroyed or heavily damaged.
Mosul is about eight times larger than Fallujah and 10 times larger than Tikrit, and ISIS is at least as potent a force as the Iraqi insurgency of 2004.
The U.S. committed over 10,000 ground troops to the assault on Fallujah, but no Western troops are expected to be available for the assault of Mosul. The Iraqi army remains weak and the Iraqi government depends heavily on militias.
Even with the full participation of those militias, backed by coalition air power, the recapture of Mosul remains a tall order. If the two are unwilling to work together, it is difficult to see how the operation can be accomplished.
In the end, the Iraqi government may be tempted to turn to the one ally that could provide both "boots on the ground" and air power, and that would have no difficulty working alongside Iraq’s Shia militias — the Islamic Republic of Iran.