WASHINGTON  A federal appeals court ruled Tuesday that a lawsuit brought by five men who say they were tortured as part of the Central Intelligence Agency’s “extraordinary rendition” program could proceed, dealing a blow to efforts by both the Bush and Obama administrations to claim sweeping executive secrecy powers.

In a 26-page ruling, the court declared that Binyam Mohamed, a British resident of Ethiopian nationality, and four other former detainees could go forward with a civil lawsuit against Jeppesen Dataplan, a Boeing subsidiary.

The former detainees said Jeppesen provided flight support when the C.I.A. transferred them to secret overseas prisons  some run by the agency and others by foreign intelligence services  where, they said, interrogators tortured them.

The Bush administration intervened, asking a judge to throw out the case because its subject matter was a state secret. The judge dismissed the case, and the men appealed. In a February appeals court hearing, the Obama administration pressed forward with the Bush administration’s stance. But a three-judge panel on the United States Court of Appeals for the Ninth Circuit said Tuesday that the executive branch’s position went too far.