Ms. Haspel is scheduled to appear before the panel for a confirmation hearing on Wednesday, and several Democratic senators have called for the Trump administration to declassify more information about her involvement in the program to inform the debate about whether she is the right fit for the post.
Mr. Mohammed’s request to provide unspecified information to the panel adds a new twist to that debate. It was described by one of his lawyers, Marine Lt. Col. Derek A. Poteet, who is helping to defend him from death-penalty charges before the military commissions system at the Guantánamo Bay naval station.
On Monday, Mr. Mohammed submitted a request to the judge overseeing pretrial hearings in that case, Army Col. James Pohl, Colonel Poteet said. While the file is not public on the commissions docket, Colonel Poteet said it consisted of an expedited motion for permission to provide the information to the committee about Ms. Haspel.
The motion, Colonel Poteet said, included an attachment, titled “Additional Facts, Law and Argument in Support,” containing “six specific paragraphs of information” from Mr. Mohammed that his client thinks the Intelligence Committee should know. After Mr. Mohammed raised the idea, his defense lawyers agreed that the information was important, he said.
“I am not able to describe the information,” Colonel Poteet said. He added that it came from Mr. Mohammed himself, not from files turned over by the government to defense lawyers about the treatment of their client in C.I.A. custody.
It is not clear whether Colonel Pohl would rule on the motion before Ms. Haspel’s hearing on Wednesday.
Asked whether Ms. Haspel had any involvement in Mr. Mohammed’s detention or interrogation, Dean Boyd, a C.I.A. spokesman, said he was prohibited from commenting on her activities in 2003 given the sensitivity of her work. But, he said, on Monday the agency had delivered a set of classified documents to the Senate that describe her 33-year career “including her time in C.I.A.’s Counterterrorism Center in the years after 9/11.” The files are available to every senator, not just committee members, he said.
He also said the American people would get a chance to hear from her directly at her confirmation hearing on Wednesday.
“She has indicated to the senators she has met with, and will reaffirm tomorrow, her commitment never to restart such a C.I.A. detention and interrogation program,” Mr. Boyd said on Tuesday. “She remains fully committed to the U.S. laws and Army Field Manuals that govern interrogation — the legal framework in place today.”
During the Bush administration, the Justice Department wrote secret memos approving C.I.A. torture techniques as purportedly lawful despite anti-torture laws. The department later withdrew those memos, and Congress enacted a law limiting interrogators to techniques listed in the Army Field Manual.
The C.I.A. inspector general later found that agency interrogators sometimes exceeded limits in the descriptions of techniques provided to the Justice Department for legal analysis. The Senate report also concluded that the C.I.A. misled the White House and other administration officials about its use of such techniques and portrayed them as more effective than they were.
Ms. Haspel ran a black-site prison in Thailand in late 2002 while a detainee being held there, Abd al-Rahim al-Nashiri, who is accused of orchestrating Al Qaeda’s attack on the American destroyer Cole off the coast of Yemen in 2000, was subjected to torture techniques including waterboarding. She was also involved in destroying videotapes of interrogation sessions in 2005.
The agency closed the Thailand prison in late 2002, and Ms. Haspel returned to the Counterterrorism Center outside Washington as a senior operations manager but continued to do temporary assignments overseas. But the details of what she was doing in 2003 are not public.
This month, four Democratic senators on the Intelligence Committee — Kamala D. Harris and Dianne Feinstein, both of California; Ron Wyden of Oregon; and Martin Heinrich of New Mexico — wrote to Daniel Coats, the director of national intelligence, asking him to declassify all C.I.A. information related to Ms. Haspel’s involvement in the program before her hearing, since she, as acting director of the agency, has declined to do so on her own.
“The American people deserve transparency regarding the background of a nominee who will be asked to represent them, and their values, around the world,” they wrote, adding: “Without making this information available to the American people, Ms. Haspel’s nomination cannot be fully and properly considered by the Senate.”