Iranian-backed Shia militias embedded alongside Iraqi security forces are now a bigger threat than the fragmented fighting power of former Islamic State extremists, a senior Canadian military commander told a House of Commons committee today.

Lt.-Gen. Mike Rouleau delivered the assessment while updating the all-party House of Commons defence committee on recent events and threats in the Middle East.

He said out of the roughly 70,000 Shia militia members under arms in Iraq, about 30,000 of them are hardcore fighters affiliated with Iran who could pose a danger.

"They are a very big concern," Rouleau tesfied. "In fact, they're my No. 1 concern. At the moment, relative to force protection, I am more concerned about that swath of Shiite militia groups than I necessarily am about Daesh (the Arabic term for ISIS) because Daesh has been defeated militarily."

The remnant of the ISIS units hiding out in remote regions of northern Iraq and Syria, he said, "are reorganizing and spending time on themselves, more than they are spending time on attack planning."

Over the last two weeks, CBC News has spoken to several senior Canadian and anti-ISIS coalition commanders who share Rouleau's assessment and note that the militias have "yet to extract their pound of flesh" for the targeted killing of Iranian General Qasem Soleimani, the commander of the secretive Quds Forces, by the U.S. in early January.

Iranian mourners gather during the final stage of funeral processions for slain top general Qasem Soleimani in his hometown Kerman on January 7, 2020. (Atta Kenare/AFP/Getty Images)

The Iranians fired ballistic missiles into two Iraqi bases used by coalition forces, including Canadians, but have thus far taken no further retaliatory action.

The militias became highly integrated with Iraqi forces during the battles to expel ISIS from the northern part of the country, including the prolonged fight for Iraq's second largest city, Mosul.

"These Shiite militia groups we're concerned about are very well equipped," Rouleau told MPs. "They have tubed artillery. They have multiple launch rocket systems and armed UAVs. They have air defence equipment."

Rather than being a ragtag force, the fighters are like armed as though they are "a state military," he said.

Canada, with roughly 500 troops in Iraq alongside the U.S.-led coalition, is keeping a close intelligence eye on the various groups to determine what their intentions might be.

"They have been muted since the attack and the U.S. threats that — if a U.S. or coalition service member dies at the hands of these group — there will be an outsized response," said Rouleau, who is responsible for all military operations, foreign and domestic.

Ongoing crises in Iran, including the COVID-19 outbreak and the fallout from punishing economic sanctions, are also helping to mitigate any possible retaliation, he added.

Conservative defence critic James Bezan said he wondered how much support there was for the Shia militias within the Iraqi government itself.

Sandra McCardell, director general of the Middle East Bureau at Global Affairs Canada, told the committee that Iraq, prior to the Soleimani killing, had been engulfed in anti-Iranian, anti-corruption protests.

"They were frustrated and resentful of the foreign influence in their country," she testified. "I think what we've seen more recently, particularly since the killing of Qasem Soleimani, is that there has been pressure to again return to sectarian camps."

After the 2003 U.S.invasion, Iraq descended into a sectarian bloodbath between Shia and Sunni Muslims.

"How we'll go from here remains to be seen," McCardell said.

Rouleau said that in the aftermath of the Iranian missile attack on Erbil, where Canadian special forces have conducted operations out of since 2014, consideration is being given to consolidating Canadian bases in Iraq.