WASHINGTON — For months, the Obama administration has refused to confirm or deny the existence of a Justice Department memorandum that approved the targeted killing of a United States citizen, Anwar al-Awlaki, who died in a drone strike in Yemen last September.

But in an exchange at a budget hearing on Thursday, Senator Patrick J. Leahy and Attorney General Eric H. Holder Jr. came close to implicitly conceding that there is indeed such a memo, which was written by the Justice Department’s Office of Legal Counsel.

Mr. Leahy, a Vermont Democrat who is chairman of the Senate Judiciary Committee, brought up a conversation he said he and Mr. Holder had earlier this week about a speech on “drones and targeting of U.S. citizens” that the attorney general delivered on Monday.

“I still want to see the Office of Legal Counsel memorandum and I would urge you to keep working on that,” Mr. Leahy said to Mr. Holder. “I realize that’s a matter of some debate within the administration but ...”