WASHINGTON — Lawyers for three men who have been imprisoned by the United States military in Afghanistan without trial for nearly a decade are renewing their quest for hearings in American courts. They say new information has emerged that undermines an appeals court ruling against them two years ago.

That information — which the lawyers are filing as documents in the United States District Court here — includes a letter by the chief of staff to President Hamid Karzai of Afghanistan declaring that the Afghan government does not want custody of the detainees and that it “favors these individuals having access to a fair judicial process, and adjudication of their case by a competent court.”

The prisoners are two Yemenis and a Tunisian who say they were captured outside Afghanistan and that they are not terrorists. They want a federal judge, John D. Bates, to review the evidence against them and, if he agrees that they are being held by mistake, to order the military to repatriate them. Detainees imprisoned at Guantánamo Bay, Cuba, already have such habeas corpus rights.

There are believed to be about a dozen such men — non-Afghans captured elsewhere — who have been imprisoned for years by the United States military at Bagram Air Base, north of Kabul.