WATCH: According to estimates released by Parliamentary Budget Officer Jean-Denis Frechette, the the price tag for the six-month mission ranges from a low of $128.8 million to a high of $166.4 million. On Monday, Defence Minister Jason Kenney said the estimated cost for the full six-month mission is approximately $122 million. Jacques Bourbeau reports.

OTTAWA — The federal parliamentary budget office said Tuesday the cost of Canada’s role in NATO’s ongoing anti-terror mission is between $7 million and $44 million more than estimates the government announced Monday.

In a report, Parliamentary Budget Officer Jean-Denis Fréchette pegged the costs for the first six months of the mission between $129 million and $166 million.

The report comes hours after Defence Minister Jason Kenney told Global News his department was seeking authority to spend $122 million for its role in the mission since troops were deployed six months ago.

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READ MORE: Price tag for Iraq mission exceeds $120M in first six months, Kenney says

Fréchette described the minister’s announcement yesterday as “bizarre timing.”

If the mission is extended for another six months, for a total of 12, costs could reach between $243 million and $351 million, Tuesday’s report suggested.

WATCH: Opposition leader Tom Mulcair wasted no time going after PM Stephen Harper during question period Tuesday – demanding to know why the government “lied” about the cost of the battle in Iraq.

The estimates from both the PBO and National Defence reflect only the costs above and beyond fixed costs such as fuel, equipment maintenance and salaries; total costs associated with similar missions have fallen between six and 18 times the incremental costs.

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For the PBO, coming up with an estimate for the ongoing Operation Impact proved quite difficult.

READ MORE: Any Canadians troops deployed to Ukraine will stay far from the front lines, minister says

“I think the Department of National Defence has been always difficult, but we’ve actually had more cooperation with DND in the past for other reports,” said assistant parliamentary budget officer Mostafa Askari. “This one was extremely difficult.”

DND repeatedly stonewalled the budget office, handing over only one standard costing manual, he said. In an effort to forge a collaborative relationship with the department, Fréchette said his staff offered to share their proposed methodology in exchange for information.

The department refused, he said, adding he’s hoping the relationship between DND and his office will shift now that there’s a new minister and deputy minister at the helm.

Missing details from Operation Impact included: composition and characteristics of personnel deployed, the amount of ammunition used, the flying hours of the various aircraft and the in-theatre arrangements for providing food and accommodation, the PBO said Tuesday.

READ MORE: Majority of Canadians support Canada’s ISIS mission, poll suggests

It is uncertain whether the special advisors who joined the task force are receiving risk pay, whether the government is flying food to the troops or purchasing it in the Middle East, and whether accommodations were pre-existing or constructed specifically for the troops.

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Reasons the department gave for refusing information included alleging the information was a cabinet confidence matter or that information was neither financial nor economic data and therefore fell outside of the budget watchdog’s purview.

Some of the refusals appear to be illegal under the law allowing Parliament to regulate internal proceedings, Fréchette and Askari said.

WATCH: Defence Minister Jason Kenney revealed on Monday the cost of Operation Impact, Canada’s mission in Iraq in the fight against ISIS.

“It is somewhat disturbing that senior officials take it upon themselves to interpret the Parliament of Canada Act … in a very narrow way that allows them to deny the information we need to inform parliamentarians,” Askari told reporters.

The Conservatives have been getting flak from all opposition parties, fending off claims the government hasn’t been forthcoming with many aspects of the anti-terror mission.

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“From the outset, the prime minister has been refusing to tell Canadians the truth about our role in Iraq,” Opposition leader Tom Mulcair said during question period Tuesday.

“Our troops were not supposed to be on the front line, they weren’t supposed to be involved in combat, but of course we now know that they are.”

Mulcair continued, suggesting the Conservatives have, yet again, misled the public — and possibly even broken the law — in refusing some information to the budget office.

In response, Prime Minister Stephen Harper said he was having difficulty grasping what, exactly, the NDP was looking for.

“The government has released the costs of the mission,” he said. “That’s very clear … I don’t know how much clearer is could be.”

Joyce Murray, the Liberal critic for national defence, said this illustrates “another way in which this government lacks transparency.”

Murray was one of two MPs who requested the estimate from the PBO. She said the fact Fréchette and his team felt stonewalled made her feel disrespected.

“We asked the PBO to do this report because we’d requested again, again and again for this information,” she said, noting some of Canada’s allies have publicly released their cost estimates.

“These are estimates. There is no reason not to provide them.”

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Though Kenney has released an estimate, he said the full costs of the mission will not be known until the troops are home, and didn’t speculate as to how the current estimates could provide a hint at any future costs.

The costs for six months in Iraq, though, have already exceeded what the government spent during its seven months in Libya.

The incremental costs for that 2011 mission were pegged at a little less than $100 million. The total cost for the mission, meanwhile, which included everything from salaries to equipment maintenance and jet fuel, reached a staggering $347 million.

Kenney said on Sunday he intended to table costs-to-date before the end of the month. On Monday, the parliamentary budget officer announced he would release his estimate of the mission Tuesday morning.

The release came as a surprise to Fréchette and the rest of his staff, he said, adding he could not offer any insight into the discrepancy between his office’s figures and those of the government.

“We have no information about the government’s figures released yesterday,” Fréchette said Tuesday. “For weeks we’ve been told we won’t have any information, then all of a sudden the figure is released after we announce we’re going to have a report.”

Before National Defence can spend the $122 million, Kenney will have to get permission from MPs and senators since this goes beyond the purse the department received for the year. This will be done through the supplementary estimates process, Kenney said.

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Once that document is tabled later this week, Fréchette said his office might be able to glean more information — depending how much data is released alongside the sum.

Canada send about 600 troops to Iraq along with six CF-18 Hornet fighter aircraft, two CP-140 Aurora surveillance aircraft, one C-150T Polaris air refueller, one C-17 Globemaster and one C-130J Hercules aircraft.

The PBO released the report after two members of Parliament in October requested estimates for incremental costs of a six-month and 12-month mission.