The Specialized Criminal Court often tries suspects accused of affiliation with al-Qaida's local branch, which operates both in the kingdom and in Yemen.
But critics say it also tries human rights activists and other dissidents as well cases related to unrest among Saudi Arabia's Shiite minority.
It was unclear if "supporting terrorism" referred to all cases tried by the court.
Spokesman Fahd bin Abdullah al-Bakran told reporters late yesterday night that the Specialized Criminal Court has already ruled in 1,080 cases and is still looking into another 419 cases that involve 2,800 suspects.