Tarek Hassan was arrested in August and charged with harming national interests. He is accused of coordinating with Syrian agents, mainly to gather information about the communications industry in the three countries and Syria's nuclear program. Two Israelis have been charged in absentia.
The prosecution called Hassan a "traitor," and accused Israel of continuing to recruit spies even in a time of peace.
The court issued the gag order to "safeguard national interests" on Saturday and adjourned the session until Sunday, when the defense team is due to present its case.
Israel has said it has no information about the case.