WASHINGTON — The arrest of a suspect in the attempted Times Square car bombing revived the volatile political debate over terrorism policy on Tuesday, as President Obama’s supporters and critics squared off over how the nation should handle those plotting against it.

The suspect, Faisal Shahzad, was interrogated without initially being read his Miranda rights under a public safety exception, and provided what the F.B.I. called “valuable intelligence and evidence.”

After investigators determined there was no imminent threat to be headed off, Mr. Shahzad was later read his rights to remain silent, but he waived them and continued talking, the F.B.I. said. Authorities charged him as a civilian on Tuesday, but postponed plans to bring him to court.

The handling of Mr. Shahzad touched off the same sort of argument that followed the attempted Christmas Day bombing of a passenger jet bound for Detroit. Some Republicans urged the Obama administration to interrogate Mr. Shahzad without affording him Miranda rights and to classify him as an enemy combatant, which would allow authorities to detain him indefinitely. But Democrats said his quick arrest and his reported confession showed the system can respond to threats of terrorism without resorting to extraordinary tactics.