Aaron Daniel Driver, who is 23, is not facing any criminal charges.
The Crown, which asserts Driver may engage in terrorism or help a terrorist group, is seeking a peace bond against him to limit his activities.
Driver did not appear in court Tuesday and the matter was put over to June 24.
Crown attorney Ian Mahon, saying evidence is still being disclosed to the defence, would not reveal details about the accusations against Driver.
Published reports have said Driver posted messages on social media that praised terrorist activities, including the attack last October on Parliament Hill by Michael Zehaf-Bibeau.
The Crown has not yet revealed what kind of restrictions it wants to impose on Driver.
Under a peace bond, judges can impose travel restrictions, set curfews, require someone to wear electronic monitoring devices or simply demand good behaviour.
People who refuse to agree to the terms or who violate them can be jailed for up to one year.