The Conservative government has signalled its intent to keep the existing Canadian Forces contingent in Iraq there for another year, and to broaden the mission to include airstrikes in neighbouring Syria.
The Opposition New Democrats want the soldiers pulled out immediately, while the Liberals suggest they could remain, but solely to train existing security forces.
Both opposition parties also called on the government to increase and expand the humanitarian support being provided to both countries.
The government will consider that, said Foreign Affairs Minister Rob Nicholson, but security must come first for the good of the region and for Canadians.
"ISIL's barbarity is an affront to human dignity and to the civilized world," Nicholson said.
"It threatens the very principles that shape Canada's national identity and guide our engagement on the global stage it's violent ideology and expansionist agenda jeopardize Canadian interests and threaten Canadian citizens."
There have been six CF-18 jets, two surveillance planes, a refuelling aircraft and 600 supporting personnel in Iraq since Parliament signed off on the first six-month deployment last fall.
But the NDP says Canada can be involved in that fight in ways that don't involve dropping bombs or training foreign fighters.
They introduced a series of amendments which, among other things, would require the Canadian Forces to stop taking part in airstrikes and training as soon as possible.
"We would take our soldiers out of the theatre," said NDP foreign affairs critic Paul Dewar.
Instead, the NDP would increase humanitarian aid in areas where there would be immediate impact, increase support for refugees, offer help for political stabilization and maintain efforts to stop foreign fighters from joining ISIL's ranks.
"We can save lives, we can build peace to help the people in Iraq," Dewar said.
The amendments don't rule out a role for the military altogether, proposing military support for the transportation of weapons to help the fight against ISIL.
Liberal defence critic Joyce Murray told the Commons that her party does see a role for soldiers. Over 1,000 Canadians worked as military trainers in Afghanistan, she noted.
"Surely Canada can do more now in Iraq, and we can and must do it away from the front lines."
A contingent of 69 elite Canadian soldiers deployed to northern Iraq last September and have since trained around 650 peshmerga fighters, but debate has persisted about how much of the training is actually putting those soldiers into combat positions.
Expanding the mission into Syria isn't on the table for either opposition party, who see it as expressly supporting Syrian President Bashar Assad.
The Conservatives argue that ISIL is using parts of Syria as a base for fighters and equipment, and can't be allowed space to regroup.
The NDP's amendments also call for the government to regularly report back on the cost of the military and humanitarian contributions.
To date, the military mission has been reported to have cost $122 million and Defence Minister Jason Kenney said Thursday that additional funds will be allocated to his department to cover the incremental costs of the mission.
The Conservatives have spent more than $100 million on assistance to Iraq, and since 2011, more than $700 million has been spent in Syria, though much of it relates to the five years of civil war that have decimated the country.
Canada could be doing more, Murray said.
"Canada can lead an international humanitarian aid intervention that is well funded and well-planned to help those who are suffering," she said.
The debate was set to continue throughout the day Thursday and resume on Monday, with a vote expected Monday night.
Liberal MP Irwin Cotler, considered one of the senior statesmen in the Commons on international rights issues, has said he will abstain again from the vote, as he did in October.
At the time, Cotler said he stayed away in part because the government had said it wouldn't bomb in Syria without the government's consent.
"I remain unable to support the government in this matter because its proposed expansion of Canada's mission continues to allow Assad to assault Syrian civilians with impunity," he said in a statement.
"Moreover, the government's lack of clarity in October has only been compounded by a lack of forthrightness since. "
The government does not need the consent of Parliament to expand the mission, but the Conservatives have made it a custom to seek support in the case of deployments.
Neither the Liberals nor the NDP intend to support the motion, although it's expected to pass nonetheless, given that the Conservatives hold the majority of the seats in the Commons.
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