On at least two occasions recently, Defence Minister Jason Kenney has mused that CF-18s could be asked to fly strike missions against extremist targets in Syria.
Harper is not ruling out that possibility.
Last fall, Parliament approved Canada's participation in U.S.-led coalition air strikes against the forces of the Islamic State in Iraq and the Levant (ISIL), but limited the involvement to Iraq and set a six-month lifespan.
The mandate runs out on April 7.
"Next week, it is the government's plan to move forward with a request for Parliament for extension and expansion of the mission," Harper said Wednesday in Mississauga, Ont.
Sources have previously told The Canadian Press that an extension would likely involve a commitment of more than six months, in part so it doesn't expire during the fall election campaign.
Last fall, the motion passed by MPs explicitly ruled out deploying ground troops for combat operations, although 69 special forces soldiers were assigned to train and advise Kurdish troops.
It's not clear how the special forces mission will be affected by next week's request.
The original Commons motion left commanders with a free hand when it came to the air campaign. But Harper, in his speech on the issue set limits by saying that strikes on targets in Syria would require an explicit invitation from the Syrian government.
"The current authorization laid open the possibility of going to Syria although we have not done that," Harper said Wednesday.
"But we'll address issues like that next week when I make a proposal to the House of Commons."
Only the U.S. and its Persian Gulf allies have flown strikes into Syria, where the dictatorship of Bashar al-Assad has been fighting both Islamic State extremists and a collection of rebel factions in a four-year-old civil war that has left over 200,000 dead.
The Americans notify Syria about air strikes, but they insist they don't co-ordinate activity. A defence source said Canada could follow a similar line, should extended missions be offered.
President Barack Obama has a war resolution before Congress, which would expand American efforts against ISIL and authorize limited, but not "enduring" ground operations.
Dave Perry, an senior analyst with Canadian Defence and Foreign Affairs Institute, said he doesn't expect the Canadian authorization to entirely mirror what's proposed in Washington, but it will be aimed at giving the government and military maximum flexibility.
New Democrat defence critic Jack Harris said it would be breathtaking if the Conservatives proposed removing geographic restrictions
"This is an invitation to a far greater conflict than anything Canadians have contemplated," he said. "They claim ISIL has declared war on Canada. That's preposterous as a notion. The implications of that for Canada and for the world would be quite astonishing."
Bombing ISIL in Syria would only strengthen Assad's position, Harris added.
The air force has six CF-18 jets bombing Islamic State targets along with two surveillance planes and an aerial tanker operating out of bases in Kuwait.
The Harper cabinet doesn't need Parliament to authorize a renewed commitment at any time, but the Conservatives have sought all-party support in the House of Commons for such missions, even if they have rarely received it.
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