One of the first clues of how the Obama administration will deal with the issue of domestic surveillance may come in a court case in Alexandria, Va., where a judge has ordered the Justice Department to turn over material from the National Security Agency and other intelligence agencies on possible eavesdropping on Ali al-Timimi, an Islamic leader convicted of supporting terrorism. The Justice Department has never acknowledged that it has used intercepts from the N.S.A. program in any criminal or civil case, which could be unlawful because the wiretaps were conducted without court warrants.

Mr. Timimi has claimed that he did not get a fair trial because prosecutors secretly used N.S.A. wiretaps in his case, and he also argues that the government has turned over to the court only intercepted conversations that make him look guilty, while withholding those that might prove he is innocent. A recently unsealed transcript, citing a closed hearing, strongly suggests that the wiretaps were used in Mr. Timimi’s criminal trial.

“We believe that the undisclosed interceptions already uncovered in this case are serious and knowing violations of federal law,” said Jonathan Turley, a lawyer for Mr. Timimi.

Meanwhile, an Islamic charity in Oregon that had its assets frozen by the Treasury Department on the ground that it was also supporting terrorism is pushing ahead with a lawsuit of its own. The Obama administration must decide whether to continue to use the state-secrets privilege in order to block the disclosure of information about any N.S.A. eavesdropping.

The charity, Al-Haramain Islamic Foundation, is charging, based in part on a classified document that the government mistakenly gave to its lawyers, that it was the target of wiretapping without warrants. Lawyers for the group say they believe that the N.S.A. listened illegally not only to the international phone calls of members of the charity itself, but also to the calls of two of its lawyers in Washington.

Mr. Eisenberg, a lawyer for Al-Haramain, said the Justice Department had frustrated efforts to develop evidence in the case both by invoking the state-secrets claim and by refusing to grant security clearances to some members of the charity’s legal team.

Image A court has ordered the government to turn over information on any federal eavesdropping conducted in the case of Ali al-Timimi, center, who was convicted of supporting terrorism. Credit... Manuel Balce Ceneta/Associated Press

“In every way, they’ve stonewalled us, and the new administration can change all that,” Mr. Eisenberg said. “They can take the blindfolds off.”