Jeffrey Labelle's father is expected to offer the court guarantees he hopes will persuade a judge to release his 21-year-old son into his custody.
Montreal police say Labelle's family tipped them off last week that he had become radicalized.
They searched his home on Friday and say they found a city map that showed the co-ordinates of four different police stations.
Police say no direct threats were made and that they arrested Labelle as a "preventive" measure.
Labelle appeared in court briefly Monday afternoon but the judge suspended the case until Tuesday to allow his father to testify.
The young man, bearded and wearing a maroon, black and yellow sweater under a black winter vest, looked confused as he stood handcuffed in the dock.
His lawyer, Julie Bernier said after the court proceedings she thought Labelle looked "stressed."
"You have to understand that he has no prior convictions and this was the first time he was in front of a court," Bernier said. "We'll see how he feels tomorrow (Tuesday)."
Even though police said it was Labelle's family who tipped them off to his alleged suspect behaviour, Bernier said it was not his father who did so.
Labelle was charged with a Criminal Code provision that allows for the arrest of someone who "commits an act that, in all the circumstances, is likely to cause a reasonable apprehension that terrorist activity is occurring or will occur, without believing that such activity is occurring or will occur."
Bernier said she will ask the court for her client to undergo a psychiatric evaluation in order to assess if Labelle can be exempt from criminal responsibly due to a mental disorder.
She would not say if Labelle's father would testify about his son's mental state.
Federal Public Safety Minister Steven Blaney said Monday he commended the Montreal police for their investigation into "all threats."
"Ongoing vigilance on the part of our law- enforcement organizations is key to ensuring the safety and security of all Canadians," Blaney said in a statement.