Two Canadian soldiers have been injured in a hit-and-run that is being investigated as a possible terror attack, with the federal government saying there are "clear indications" the suspect in this incident "had become radicalized."

The Prime Minister's Office, which played a key role in making the terror allegation public, said the individual under investigation was known to counter-terrorist and law-enforcement officials before the car struck the soldiers Monday about 50 kilometres southeast of Montreal.

The suspect, whom law enforcement sources identified as 25-year-old Martin Couture-Rouleau, is dead.

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He was shot multiple times by local police in Saint-Jean-sur-Richelieu, Que., after a police pursuit. Mr. Couture-Rouleau lost control of his car during the chase and it rolled over. News reports say he brandished a knife before being shot.

He died of his injuries, according to the Quebec provincial police.

The soldiers were hit while they were walking late Monday morning in a shopping mall parking lot, a few kilometres from the Collège militaire royal de Saint-Jean, the military academy operated by the Department of National Defence.

The man accused of running them over, Mr. Couture-Rouleau, was the president of a pressure-washing company that was incorporated in 2012, according to Quebec corporate records.

Late Monday, a Sûreté du Québec provincial police van was posted outside his family home, one of several bungalows in a subdivision near the crime scene. Residents there said he had changed his religion more than a year ago.

"We knew he had converted to Islam, but it didn't go any further as far as we knew," said a neighbour, who declined to identify himself. He said Mr. Couture-Rouleau had grown a beard and had taken to wearing baggy clothing and a head covering.

On a social media site for Muslims ("Ummaland"), Mr. Couture-Rouleau appears to have identified himself as "Ahmad the convert." (The posted birthdate, March 1, is consistent with what sources say is his birthday.)

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One source said Mr. Couture-Rouleau had demonstrated extremist behaviour that had drawn federal officials' suspicion – but he was not considered a top target.

One of the soldiers is in critical condition in hospital and authorities are "fearing for his life," according to the SQ. The other victim suffered more minor injuries. Their names have not yet been released.

Within hours of the incident, the Harper government went public with the allegation the hit-and-run may have been the act of a terrorist.

On Monday afternoon, Conservative MP Randy Hoback rose during Question Period and asked Prime Minister Stephen Harper a question on "a possible terrorist attack" against soldiers in what was clearly a prearranged exchange. Mr. Harper said it was "obviously extremely troubling."

The Prime Minister's Office later announced Mr. Harper had in fact been briefed beforehand on the matter by RCMP Commissioner Bob Paulson, Chief of Defence Staff General Tom Lawson, and National Security Adviser Stephen Rigby.

The incident occurred on the eve of Canadian warplanes departing for an Iraq air combat mission in which they will join an international coalition launching air strikes on extremist Islamic State militants in the region.

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Official Opposition Leader Thomas Mulcair said the government erred in raising the suspected terror link in the Commons.

"I think it's a mistake to start drawing conclusions on such limited information, especially as to motive. So I was a bit surprised by the interplay between the Prime Minister and one of his backbenchers when we're still waiting for any information from the police. Let the police do their job and then we'll know whether we're dealing with the type of situation they've described."

The government is also poised to table a counter-terrorism bill this week, according to a source familiar with the issue. Public Safety Minister Steven Blaney has said the bill will give Canada's spy agencies new powers to track Canadians abroad and share intelligence with other countries. It's the first substantial change to the Canadian Security Intelligence Service Act since the agency's creation 30 years ago and comes as the agency has complained that recent court rulings have hindered its powers.

The SQ is investigating Monday's incident and still documenting the exact chronology.

SQ spokesman Lieutenant Guy Lapointe said the investigation will explore the possibility that the driver deliberately targeted the two soldiers.

"A deliberate act is part of the things we will be looking at. But it's very early right now to hypothesize or speculate as to what the intentions were," Lt. Lapointe said. A police source said that scenario of a deliberate attack against the military "is not far-fetched."

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The RCMP said in a statement that the suspect was known to authorities who were concerned he'd become radicalized.

"Out of respect and deference to the ongoing criminal investigation arising from today's terrible events the RCMP will not comment further except to say that we are working with our law enforcement partners to ensure all avenues of investigation are pursued."

The SQ is overseeing the investigation after local police used their weapons to stop the suspect.

With reports from Tu Thanh Ha, Colin Freeze and Josh Wingrove