The arrest of Abdullah al-Muhajir on 8 May at Chicago's O'Hare international airport was announced by the US Government on Monday.
Representing Mr al-Muhajir, defence lawyer Donna Newman has filed a petition questioning the legal basis for classifying her client as an enemy combatant - a term which allows for his indefinite detention without trial.
"He is being detained without time limit, or the right to counsel. There aren't any formal charges and that is why the defence community is outraged," she said.
A district court judge said he would consider Ms Newman's request on Wednesday, but it wasn't clear whether the court has any jurisdiction in the case now that the suspect is in military custody.
President George W Bush said on Tuesday that there was a "full-scale manhunt on" for anyone else believed to be involved in the alleged al-Qaeda plot to detonate a radioactive bomb in the US.
Military detention
Mr Bush said Mr al-Muhajir, born Jose Padilla, had links to the al-Qaeda terror group, which the US blames for the 11 September attacks in New York and Washington.
How does a dirty bomb work?
A conventional bomb is packed with radioactive isotopes
The force of the explosion spreads radioactive material over a wide area
Likely to cause radiation sickness in any exposed to the contaminated area
Massive disruption ensues
"This guy, Padilla, is a bad guy. And he is where he needs to be detained," Mr Bush said.
Mr Bush said that US authorities are now hunting down any terror associates Mr al-Muhajir may have.
"As we run down these killers or would-be killers, we'll let you know," he said.
Mr al-Muhajir, a US citizen of Puerto Rican descent, has been handed over to the army and is being detained at a military facility in South Carolina.
Legal quagmire
The BBC's correspondent in Washington, Alex Van Wel, says US lawyers are describing Mr al-Muhajir's case as a "legal twilight zone" and say there are no precedents which they can apply to work out what his position might be.
Our correspondent says civil rights groups are accusing the US of changing Mr al-Muhajir's status simply in order to detain him indefinitely without bringing a charge.
The suspect is alleged to have been planning to build and explode the bomb, which can spread material highly toxic to humans.
Investigators are said to have known about Mr al-Muhajir for some time.
Officials said he was stopped in the "initial planning stages" and no specific targets had been selected.
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