Aaron Driver, who is 23, is not accused of any crime, but federal authorities are trying to limit his activities on suspicion that he might help or engage in terrorist activities.
Driver has launched a challenge under the Charter of Rights and Freedoms.
He was in court Tuesday, quietly reading the Qur'an while lawyers discussed the case.
The matter was put over to July 20, when a date may be set for the challenge.
Driver is out on bail, provided he stay in Winnipeg, possess no computers, own no objects with Islamic State logos or slogans and avoid social media.