Conservatives have long disliked the Miranda ruling, which is intended to ensure that confessions are not coerced. Its use in terrorism cases has been especially controversial because of concerns that informing a suspect of his rights could interrupt the flow of the interrogation and prompt him to stop disclosing information that might prevent a future attack.

Rudolph W. Giuliani, the former New York City mayor and Republican presidential candidate, said Sunday on “This Week” on ABC that he supported Mr. Holder’s proposal. However, he also suggested that enacting it would not quell conservative criticism, arguing that it would be even better to hold suspects like Mr. Shahzad as military detainees for lengthier interrogation.

“I would not have given him Miranda warnings after just a couple of hours of questioning,” Mr. Giuliani said. “I would have instead declared him an enemy combatant, asked the president to do that, and at the same time, that would have given us the opportunity to question him for a much longer period of time.”

Any effort to further limit the Miranda rule will be likely to face challenges. In a 2000 case, the Supreme Court voted 7 to 2 to strike down a statute that essentially overruled Miranda by allowing prosecutors to use statements defendants made voluntarily before being read their rights.

Despite the political furor over reading terrorism suspects their Miranda rights, it is not clear that doing so has had a major impact on recent interrogations.

For example, even after Mr. Shahzad was read his rights, he waived them and continued talking. With Mr. Abdulmutallab, who is accused of trying to light a bomb hidden in his undergarments, the pre-Miranda interrogation lasted until he was taken into surgery for the burns he suffered. Afterward, he did not resume cooperating and was also read his Miranda rights, although the sequence of events is uncertain. Relatives later persuaded him to start talking again.

In Congressional testimony last week, Mr. Holder defended the legality of the delays in both cases, noting that the Supreme Court had set no time limit for use of the public-safety exception. But on Sunday, he seemed to indicate uneasiness about the executive branch unilaterally pushing those limits, and called for Congressional action to allow lengthier interrogations without Miranda warnings in international terrorism cases.