The facility - part of the CIA's network of secret so-called "black prisons" - was reportedly financed by the CIA but managed by Moroccan authorities.
The Yemen-born Binalshibh remains a prisoner in the US detention facility in Guantanamo Bay, Cuba. Thomas Durkin, his civilian lawyer, called the tapes "extremely relevant" to his client's case.
One other suspect - Binyam Mohamed, detained in Pakistan in 2002 - is known to have been transferred to a Moroccan jail.
'No evidence' of torture
American officials said the tapes do not show evidence of torture, and the fact that the CIA confirmed the tapes' existence suggests they do not contain any incriminating footage.
Morocco does have a history of rights violations against detainees, however: The US state department's latest human rights report on Morocco documents numerous allegations of "security forces [who] tortured and abused individuals in their custody".
Some of the tapes destroyed in 2005 do show agents waterboarding two other alleged al-Qaeda operatives, Abu Zubaydah and Abd al-Nashiri. A federal prosecutor is investigating the destruction of those tapes.
"Today's report is a stark reminder of how much information the government is still withholding about the Bush administration's interrogation policies," Alexander Abdo, an attorney with the American Civil Liberties Union, said.
George Little, a CIA spokesman, declined to comment on the Moroccan facility.