James Bezan, Conservative MP for Selkirk-Interlake, and Canada's parliamentary secretary of defence, said the 23-year-old Winnipeg-based ISIS supporter made detestable comments in an interview.
"I believe that he should be charged again for promoting attacks against Canadian members of the armed forces, as well as against our police officers," Bezan said.
"I think that's despicable. You've got to remember we're in Canada here and I would be shocked to see someone actually promote that type of criminal behaviour. And that's exactly what Aaron Driver is doing."
In the interview, Driver told CBC that Canada deserved to be targeted by Michael Zehaf-Bibeau for its role in war in the Middle East.
On Oct. 22, Zehaf-Bibeau shot dead Cpl. Nathan Cirillo, who was standing guard at the National War Monument in Ottawa, then charged into Parliament Hill in Ottawa before he was gunned down.
Bezan wants police to review Driver's comments and lay criminal charges against him.
Watched by CSIS
Driver caught the attention of CSIS, Canada's spy agency, in October 2014 when he was tweeting his support for ISIS.
That activity landed him on a watch list.
Driver regularly shared his pro-ISIS views on social media and was regularly shut down by Twitter for doing so. He was arrested by RCMP on June 4 and investigators searched his home, removing what appeared to be computer towers.
After eight days in custody, Driver was released on bail under 25 strict conditions, including surrendering his passport, obeying a curfew of 9 p.m. to 6 a.m., and being prohibited from using a computer or smartphone or logging into social media accounts.
Threat or no threat?
Mubin Shaikh, a former counter terrorism operative for CSIS, says Driver is someone to be very concerned about.
Driver states he is not a threat but then he talks about why he thinks it's justified to target non-Muslims for attack. That proves he is still very much a threat, Shaikh said.
"He is most definitely a threat, what he's suggested actually is a very well-rehearsed recruiting line. This is something that is shared across the board," Shaikh said.
"He is re-enforcing and regurgitating the recruitment narratives that make individuals commit these attacks."
Shaikh said police are justified in monitoring Driver because of that.
However, another expert on terror threats has had researchers monitor Driver's online activity and does not see him as an immediate threat.
"Driver explicitly stated that he is not a threat and he does not intend to get involved with any action. On the face of it, that's a credible claim," said Lorne Dawson, a professor of at the University of Waterloo and co-director of the Canadian Network for Research on Terrorism, Security and Society.
Research into radicalized individuals shows they rarely move beyond just talking about it, he said.