The administration’s flirtation with the ideas follows the arrest last week of Faisal Shahzad, the suspect in the failed attempt to detonate a car bomb in Times Square. Federal interrogators questioned Mr. Shahzad for several hours before warning him that he had right to remain silent and consult a lawyer, citing an exception to the Miranda rule for immediate threats to public safety.

Image Anthony Romero, of the A.C.L.U., opposes the plan. Credit... Jonathan Ernst/Reuters

Officials have said that Mr. Shahzad waived those rights, as well as his right to a quick initial hearing before a judge, and has continued cooperating with interrogators. But, worried that suspects in future cases may not do likewise, or that law enforcement officials will be confused about the rules, the administration has decided to push for changes.

There is a federal rule of criminal procedure that requires law enforcement officials to take a prisoner to a judge for an initial hearing “without unnecessary delay.” But specialists in criminal law said it would be a fairly simple matter for Congress to pass a statute exempting terrorism cases.

But they said it would be trickier to get around a Supreme Court precedent that governs when people must get initial hearings before a judge in cases in which the police have arrested someone without a warrant. The court has ruled that such prisoners must generally get a hearing within 48 hours to ensure there is probable cause to believe they committed a crime.

Congress has no authority to override the Supreme Court’s constitutional rulings. But several legal specialists said the court might be more willing to approve modifications if lawmakers and the executive branch agreed that the changes were necessary in the fight against terrorism.

One idea, Mr. Wittes said, would be for prosecutors to ask a judge for permission to continue holding a terrorism suspect who had been arrested without bringing the prisoner to the courtroom. As a safeguard, he said, Congress could require a high-level Justice Department official to certify that delaying the suspect’s initial appearance in court was necessary for national-security reasons.

The Obama administration’s consideration of the proposal comes against the backdrop of Republican attacks for its decision to handle some terrorism cases in the criminal justice system instead of declaring the suspects to be “enemy combatants” and holding them in military detention.