A US judge blocked America's most high-profile terror detainee on Tuesday from testifying in a New York courtroom to defend Osama bin Laden's son-in-law.

"I have considered this very carefully. It's much ado about nothing. It's not admissible," Judge Lewis Kaplan told the southern district court in Manhattan.

Suleiman Abu Ghaith, who married bin Laden's daughter Fatima, is on trial for conspiracy to kill Americans, conspiracy to support and supporting terrorists.

The 48-year-old from Kuwait denies the charges. He faces life imprisonment if convicted by a jury at the trial, which is expected to conclude within days.

His defense lawyers extracted 14 pages of written testimony from Khalid Sheikh Mohammed, the self-styled 9/11 mastermind held at Guantanamo Bay, saying that it disputed key elements of the prosecution's case.

Mohammed had claimed Abu Ghaith never played a military role in Al-Qaeda and had nothing to do with a 2001 plot to bomb a transatlantic US passenger jet.

He refused to testify by audio or video-link from the US military prison but government prosecutors said even a deposition would be irrelevant and prejudicial.

Kaplan, who at one point asked whether he had the right to subpoena Mohammed, ruled there was "nothing at all" in the 14 pages that would be admissable.

"The application is denied. It is in my view baseless, entirely baseless," the judge told court.

Kaplan said there was no evidence that Abu Ghaith ever met Mohammed, nor that the two had any dealings on the December 2001 shoe bomb plot, hatched in Afghanistan at a time when Mohammed may have been in Pakistan.

"There is not even evidence in this document that Khalid Sheikh Mohammed was in the same country as the defendant during the relevant period," Kaplan said.

"Does he address what Suleiman Abu Ghaith knew or didn't know? He doesn't touch it. Not even with a 10-foot pole," he added.

Mohammed's responses to written questions were vetted by US intelligence and submitted to Abu Ghaith's lawyers last Thursday.

Abu Ghaith is most famous for appearing in a video with bin Laden the day after the 9/11 attacks.

The prosecution says he was hired to recruit young men all over the world for Al-Qaeda.

The defense argues that, while Abu Ghaith made incendiary remarks, he did not conspire to kill Americans and was not involved in the shoe bomb plot.

Abu Ghaith is the most high-profile alleged Al-Qaeda member to face trial in a US federal court rather than at Guantanamo Bay, which the White House has promised to close.

US prosecutors say Abu Ghaith worked for Al-Qaeda until 2002, when he fled Afghanistan for Iran. He was captured in 2013 and brought from Jordan to the US.