"The individual who struck the two CAF members with his car is known to federal authorities, including the Integrated National Security Enforcement Team," said a statement from Jason MacDonald, Stephen Harper's communications director.
"Federal authorities have confirmed that there are clear indications that the individual had become radicalized."
Harper was briefed on the incident Monday afternoon by RCMP Commissioner Bob Paulson; Tom Lawson, the country's top military commander; and national security advisor Stephen Rigby.
Earlier in the day, Quebec provincial police said the motorist died from gunshot wounds and that he had hit two members of the Canadian Forces with his car in an incident one MP cited in the Commons as a "possible terror attack."
Lt. Michel Brunet said the 25-year-old in Saint-Jean-sur-Richelieu, southeast of Montreal, was known to authorities.
Several media outlets cited law enforcement sources as naming the suspect as Martin Rouleau, though police would not confirm the suspect's identity to The Canadian Press.
One of the two people hit was listed in critical condition, while the other's injuries were described as less serious.
News of the incident surfaced in the Commons when Conservative MP Randy Hoback asked Harper to update the House about "unconfirmed reports of a possible terror attack" against two members of the Canadian Forces.
Harper said he was aware of the reports and called them "extremely troubling."
"First and foremost our thoughts and prayers are with the victims and their families; we're closely monitoring the situation and obviously we will make available all of the resources of the federal government," he told the House.
Provincial police spokesman Joyce Kemp said it was "really premature" to speculate on any possible motives.
"We've just started the investigation, so it will take a certain time before we can say it was something accidental or deliberate," Kemp said in an interview.
NDP Leader Tom Mulcair also said he believed the government's immediate analysis to be premature.
"I think we need to be extremely careful before drawing conclusions. When (the Hoback question was asked), I said to myself, 'Come on, let the police do their work'," he told a news conference in Ottawa.
Provincial police spokeman Guy Lapointe said the shooting occurred after the man hit the two pedestrians in the parking lot of a shopping mall and took off.
That triggered a chase that ended with the man losing control and his car rolling over several times.
Police would not confirm several media reports the man was brandishing a knife when he emerged from the car.
"I can confirm to you that the two people who were struck by the car were members of the Canadian Forces," Lapointe told a news conference.
The MP for Saint-Jean, Tarik Brahmi, issued a statement following the incident.
"This is a tragic event and my thoughts go first and foremost out to the members of the Canadian Forces who were injured and to their families," the NDP MP said.
"I wish them a speedy recovery. The allegations surrounding this hit-and-run are serious and I have full confidence in provincial police investigators being able to shed light on the circumstances surrounding this event.
"In the meantime, let's allow the police to do their work and let's avoid jumping to conclusions."
Security sources said the the two Canadian Forces members were leaving the Integrated Personnel Support Unit in Saint-Jean.
Such centres provide services and support to ill and injured members of the military and their families. They also help organize transition for those leaving the Forces.
The suspect was apparently known to police and security officials, said security sources, who were not authorized to talk to the media.
But it is too soon to draw a link between the incident, Canada's unfolding mission in Iraq and threats made by the Islamic State, which called on Islamic extremists to attack members of the military and civilians in this country.
On Oct. 10, Lawson warned members of the military to be vigilant and suggested a security review for defence installations was in the offing, if the threats became specific.
"We all have to be alert to things that might be out of the normal," he said in a statement. "If something doesn't feel right, take the initiative to let the authorities know.
"We review our force protection posture on a continuous basis, and if additional measures need to be implemented, direction will be provided by Commander (Canadian Joint Operations Command)."
As late as Friday, he warned indirectly about the possible threat of terrorist retaliation for Canada's involvement in the war against ISIL.
"While ISIL represents a tremendous threat to people on the ground in Iraq and in Syria, they have also made it clear they would aspire to present a threat to the people of the nations that are providing forces for the efforts against them," he said.
"We watch that very closely, as do the security agencies here in Canada. There is no indication of direct threats, yet."