But Sen. Carl Levin, D-Michigan, chairman of the Senate Armed Services Committee, said Saturday that the suspect should not be held 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, as it has been consistently interpreted by all three branches of our government," he said.
"In the absence of such evidence I know of no legal basis for his detention as an enemy combatant. 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."
Alan Dershowitz, a prominent defense attorney and Harvard law professor, scoffed at the Republican senators' statement.
"Impossible. There's no way an American citizen committing a domestic crime in the city of Boston could be tried as an enemy combatant," he told CNN's Piers Morgan. "It could never happen. And that shows absolute ignorance of the law."
Dershowitz also said statements made by police in Boston seems to contradict the government's reasons for invoking the public safety exception.
"The police have said there's no public safety issue; it's solved, it's over," Dershowitz said. "There are no further threats. But the FBI is saying there's enough further threats to justify an exception."
Former New York Mayor Rudy Giuliani said the federal government may have known about international threats about which state officials were not aware.
"You would have to know the internals of what they have before you can assess whether there is a sensible invocation or not," Giuliani said.
If the government had prior knowledge of Tsarnaev's activities, it hasn't disclosed it. It did say that Tamerlan Tsarnaev had been on the FBI's radar in the past.
FBI agents interviewed Tamerlan two years ago and also looked at his travel history, checked databases for derogatory information and searched for Web postings. The agency found no connection with terror groups, an FBI official told CNN.
Two key Republicans on the House Homeland Security Committee -- Rep. Mike McCaul of Texas, the panel's chairman; and Rep. Peter King of New York -- will press the Obama administration for details about the FBI's questioning of Tamerlan Tsarnaev, according to a GOP congressional source.
Tamerlan Tsarnaev, who was not a U.S. citizen, traveled to Sheremetyevo, Russia, in January 2012, according to travel records provided by a U.S. official. He returned six months later.
Federal or state trial?
Dershowitz said there are many arguments that can be made to try the case in state court. It may be hard for a prosecutor to prove which crimes were committed by Tsarnaev or his older brother, Dershowitz said.
"If he says my intent was to please my brother, they could raise the question of federal jurisdiction," Dershowitz said.
This fight over federal or state jurisdiction could mean life or death.
Massachusetts does not have the death penalty.
There's another big question: The National Defense Authorization Act of 2012 requires temporary military custody of certain terrorist suspects, but Dzhokar Tsarnaev is a U.S. citizen, and the act doesn't apply to Americans.
What is the reaction in the suspects' homeland?