Immigration Minister Jason Kenney suggested Friday that the Tunisian-born man, who had been studying in Canada, could not actually have entered from here.
"When we became aware of security concerns, he was back in Tunisia, and his study permit was not renewed," Kenney told a news conference.
Ahmed Abassi was arrested last month in the U.S. and accused of planning an "act of international terrorism." He is accused of having ties to one of the two men suspected of plotting an attack on a passenger train in Ontario. He has pleaded not guilty.
The ties to Canada were being downplayed in Ottawa.
Given the economic importance of Canada-U.S. border movement, the federal government is sensitive about the country's interests being damaged by security concerns.
This country has been repeatedly, and erroneously, linked over the years to some of the 9-11 suspects and the Canadian government has aggressively combatted misinformation about terrorist ties.
Kenney addressed that general theme Friday.
"I think Canada has, frankly, had much less serious problems with terrorist-related security threats, home-grown terrorism than many other Western countries — including the United States," Kenney said.
"Having said that, we can and must not be complacent."
Initial reports, citing U.S. officials, said Abassi had travelled from Canada to the U.S. in mid-March, where he was arrested at JFK airport on April 22 — the same day Canadian authorities arrested Chibeb Esseghaier and Raed Jaser, 35 of Toronto.
Prosecutors allege Abassi had "radicalized'' Esseghaier, a Montreal resident who is one of two men charged with plotting to attack a Via Rail train.
They also say Abassi was pushing for a different plan that would contaminate the air or water with bacteria and kill up to 100,000 people.
Laval University in Quebec City held a brief news conference regarding its former student.
The event consisted of the university rector reading a 48-second statement in French, repeating it in English, and saying there would be no further comment.
He said Laval University is co-operating with authorities in the investigation.
"All we can do is express our surprise and assure the media, and the whole public, that we will collaborate with the authorities leading this investigation," said Denis Briere, the university rector.
"As for Mr. Abassi's identity, as with any request for information on a student at Universite Laval, we are held to confidentiality in personal information."
He repeated in Canada's other official language, then left.
Students were more voluble Friday. They chatted with reporters who visited the campus, where Abassi reportedly studied chemical engineering.
Some speculated about what might cause people to support terrorism.
"Radicalism results, in part, from the fact that these people are labelled and pushed into the margins," said Marie Tardif-Drolet, a student in mechanical engineering.
"That contributes to radicalizing them and it's not a good thing."
A Moroccan-born civil engineering student blamed a pair of different factors: weak-minded people — and also U.S. foreign policy.
"Islam can, like any ideology, be a source of radicalism and sadly, these days, it's Islam getting the attention," said Mohamed Amine Alaoui, a civil-engineering student.
"But for me, as with any ideology, any weak individual can be manipulated. That doesn't mean Islam is any more dangerous than any other ideology."
He also blamed U.S. policies which he said fuelled "deep injustices" in the Middle East.
"You can't ignore that aspect of the problem," Alaoui said. "The United States is not fair in its approach there. And ill-advised, or impulsive, people will tend to develop that kind of (radical) reaction."
Alaoui said news like this week's is unwelcome by the Muslim community, which must live with the fallout. He said other members of the community try to show an example and demonstrate that they are integrating well into society and trying to do some good.
Tardif-Drolet agreed that it would be wrong to cast aspersions on all Muslims, Arabs and Persians.
-With files from Stephanie Levitz in Ottawa, and Alexandre Robillard, Patrice Bergeron and Martin Ouellet in Quebec City