The move marks the first major salvo of a landmark legal battle in which lawyers defending Sulaimain Abu Ghaith will seek to challenge the US government's conduct in the "war on terror."
Ghaith was detained by US agents in Jordan at the end of February and flown to New York. He was indicted on March 1 on a single count of conspiracy to kill US nationals.
That move was decried by prominent Republicans who said he should have been treated as an enemy combatant and sent to Guantanamo Bay.
In a speech which cited in the US government indictment, Abu Ghaith defended the attacks and warned Americans that the "storms shall not stop, especially the airplanes storm."
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His defence team argues that Abu Ghaith effectively has been declared guilty -- on the basis of his "mere association" with bin Laden -- of a crime that carries a maximum sentence of life imprisonment.
They deny that his fiery rhetoric reflects direct involvement in any plot to kill Americans.
The objections relate to Abu Ghaith's interrogation on the flight from Jordan to the United States, allegedly in conditions amounting to torture.
His attorneys allege US collusion in his detention in Iran between late 2002 and early 2013, the killing of potential witnesses in US drone attacks and other assassinations of Qaeda militants, including that of bin Laden himself, and the compromising of other witnesses by the well-documented use of torture at Guantanamo.
His attorneys also argued that the terms of the indictment are so vague that Abu Ghaith's constitutional right to be made aware of the detailed charges against him have been infringed.
Abu Ghaith's counsel also asked the judge to rule inadmissible a 21-page FBI report largely based on the defendant's statements made during his 13-hour in-flight interrogation.