NEW YORK — A federal judge has ruled that President Obama’s administration doesn’t have to publicly disclose its legal justification for the drone attacks and other methods it has used to kill terrorism suspects overseas.

Two New York Times reporters and the American Civil Liberties Union (ACLU) filed a 2011 request under the Freedom of Information Act that sought any documents in which Department of Justice lawyers had discussed the highly classified “targeted-killing” program.

The requests followed a drone strike in Yemen that killed an al-Qaida leader, Anwar al-Awlaki, who had been born in the U.S. That attack prompted complaints from some law scholars and human-rights activists that, away from the battlefield, it was illegal for the U.S. to kill American citizens without a trial.

The requests for documents were turned down, on the grounds that releasing any details about the program, or even acknowledging that documents on the subject existed, could harm national security.

In a decision signed Wednesday, U.S. District Judge Colleen McMahon chided the Obama administration for refusing to provide the documents but said she had no authority to order them disclosed.

“I find myself stuck in a paradoxical situation in which I cannot solve a problem because of contradictory constraints and rules — a veritable Catch-22,” the judge wrote. “I can find no way around the thicket of laws and precedents that effectively allow the executive branch of our government to proclaim as perfectly lawful certain actions that seem on their face incompatible with our Constitution and laws, while keeping the reasons for their conclusion a secret.”

The judge kept one small part of the ACLU’s document request alive, pertaining to two Department of Defense documents that are not classified, but said she was obligated to reject the remainder of the requests because of national-security secrecy rules.

Part of her opinion was filed under seal, unable to be seen even by lawyers for the newspaper and the ACLU, and may be read only by people with security clearance.

A spokesman for the Department of Justice declined to comment.

A newspaper official said an appeal is planned.