Elizabeth May is betting they were "isolated, disturbed and deeply troubled men who were drawn to something crazy."
Tom Mulcair and Justin Trudeau are urging people to wait for the police to conclude their investigations before jumping to any conclusions.
Federal political leaders are united in condemning this week's cowardly cold-blooded killing sprees that left two unarmed Canadian soldiers dead, the halls of Parliament riddled with bullets and MPs in fear for their lives.
But they don't agree on where to draw the line between what constitutes terrorism and what is an act of senseless violence.
From the prime minister's perspective, there can be no doubt: Michael Zehaf Bibeau and Martin Couture Rouleau were terrorists. He links their respective rampages to Canada's involvement in the U.S.-led bombing campaign against Islamic extremists in Iraq.
"We are all aware and deeply troubled that both of this week's terrorist attacks were carried out by Canadian citizens, by young men born and raised in this peaceful country," Harper told the House of Commons on Thursday.
What "weakness of spirit" turned them against their country "is a question for another day," he added.
"For now, make no mistake, even as the brave men and women of our armed forces are taking this fight to the terrorists on their own territory, we are equally resolved to fight it here."
Zehaf Bibeau gunned down a ceremonial honour guard at the National War Memorial on Wednesday, before dashing over to Centre Block on Parliament Hill, where he was killed in a wild shootout with security officials in the hall of honour.
Two days earlier, Couture Rouleau deliberately plowed his car into two soldiers in Quebec, killing one. He too was shot dead by police following a car chase.
Harper used the two incidents to justify his contention that Canada's laws need to be beefed up to give police more powers to track, detain and arrest suspected terrorists. Promised legislation on that front will be expedited, he said.
While Mulcair and Trudeau did not directly challenge Harper's contention that the incidents constitute terrorism, nor did they endorse it.
The attack on Parliament Hill "was meant to embed within our minds an image of terror," Trudeau said.
But he warned against elevating the status of the killers.
"The individuals who committed these awful acts are not larger than life. They are not giants. They are certainly not martyrs. That is how they would like us to see them but it is not what they are. Seeing them that way lets the fear they try to perpetuate grow."
Green party Leader May was more direct.
"If I were a betting person ... I would put money on these being the acts of isolated, disturbed and deeply troubled men who were drawn to something crazy," she told the Commons, prompting some audible grumbling from the Conservative benches.
"I do not believe that it was a vast network or that the country is more at risk today than it was last week."
May acknowledged her hunch could be wrong and urged all MPs to "wait for answers from the police before we make any assumptions about motivations, connections or the extent of what we face."
In an interview later, May said there seems to be "an amateur randomness" to both incidents. While Zehaf Bibeau may have been inspired by Couture Rouleau's attack, and both appear to have been drawn toward radical Islamism in a bid to find some sick, twisted purpose to their lives, May said:"This isn't our 9/11, let's get over being over-dramatic about this."
"All we know is that some deranged young men ... murdered people in broad daylight and were killed shortly after. Was that their plan, why did they do it, how different is it from the murderous, suicidal and maniacal rages that make someone walk into a school and kill toddlers?
"What are we dealing with here? And until we know what we're dealing with, we can't jump to conclusions."
By concluding immediately that the incidents were acts of terrorism, May said she's concerned the government response will be inappropriate and do nothing to prevent other unbalanced young people from adopting a perverted form of Islam to justify going on a killing spree.
Trudeau later said he's waiting for the police to determine the details of what motivated the killers to commit what he called "tragic crimes."
"Whether they are more than that, I look forward to finding out."
Mulcair did not address the matter Thursday but an aide pointed to the leader's skepticism earlier in the week, after Harper declared the hit-and-run incident in Quebec to be an act of terrorism.
At that time, Mulcair refused to jump to conclusions until the police finish their investigation. And he expressed hope that Harper wasn't trying to fuel the perception of a homegrown terrorism crisis in order to justify the Canadian combat mission in Iraq or to burnish his leadership credentials heading into next year's election.
"I certainly hope that that's not what the prime minister of Canada is doing, latching onto this type of crisis to help himself," Mulcair said.