Lawyers for the five men charged in the September 11th attacks want legal proceedings put on hold during the Muslim holy month of Ramadan.
Defense attorneys are also asking that no court sessions be held on Fridays when many devout Muslims try not to work.
The defense lawyers said the court at Guantanamo Bay, Cuba has an obligation to respect the men's faith and their need to fast and pray during Ramadan.
Prosecutors said a blanket restriction would make it too difficult to schedule hearings.
The next hearing is set to start in August during Ramadan.
The five defendants held at Guantanamo Bay include Khalid Sheikh Mohammed, the self-proclaimed mastermind of the attacks.
All face the death penalty if convicted.