The suspect, Dzokhar Tsarnaev, a 19-year-old naturalized US citizen, was in hospital to receive treatment for injuries he sustained during a shootout with police on Friday.
Massachusetts Governor Deval Patrick said the seriously wounded Tsarnaev was "not able to communicate yet," hinting that he may not have been questioned so far.
But rights advocates were quick to express concern over possible efforts by President Barack Obama's administration to use a provision waiving the need to inform Tsarnaev of his right to an attorney or to remain silent.
American Civil Liberties Union executive director Anthony Romero called for a narrow read of the "public safety" exception, which is only allowed in cases where there is a "continued threat" to public safety.
"We must not waver from our tried-and-true justice system, even in the most difficult of times," he said in a statement.
"Denial of rights is un-American and will only make it harder to obtain fair convictions."
US Attorney Carmen Ortiz told reporters after Tsarnaev's arrest that the authorities had invoked the public safety exception and delayed reading him his rights, or Miranda warning.
Republican lawmakers have gone a step further, arguing that Tsarnaev, an ethnic Chechen who lived in the United States for a decade, should be declared an "enemy combatant," the same legal status as detainees being held at the Guantanamo military prison.
"A decision to not read Miranda rights to the suspect was sound and in our national security interests," read a joint statement by Senators Lindsey Graham, John McCain, Kelly Ayotte and Representative Peter King.
"However, we have concerns that limiting this investigation to 48 hours and exclusively relying on the public safety exception to Miranda could very well be a national security mistake."
But Senate Armed Service Committee Chairman Carl Levin, a Democrat, disagreed and expressed full confidence in the US justice system to try the suspect in federal civilian courts.
He warned that there was "no legal basis for his detention as an enemy combatant."
"I am not aware of any evidence so far that the Boston suspect is part of any organized group, let alone Al-Qaeda, the Taliban or one of their affiliates -- the only organizations whose members are subject to detention under the Authorization for Use of Military Force," Levin said.
"To hold the suspect as an enemy combatant under these circumstances would be contrary to our laws and may even jeopardize our efforts to prosecute him for his crimes."
Tsarnaev was caught after a massive manhunt that saw his older brother and fellow suspect Tamerlan killed.
A 1966 Supreme Court ruling requires that police read suspects their Miranda rights, in order to protect them against involuntarily incriminating themselves.
Under normal rules, only comments made by a suspect who has been read his rights is able to be used in a subsequent trial.
The court created an exception in 1984 allowing police to interrogate a suspect without reading the rights if there is deemed to be an immediate threat to themselves or to the public.
In a 2010 policy memo, the FBI ordered agents to interrogate suspected "operational terrorists" about immediate threats to public safety without first advising them of their Miranda rights.