The memo said that three conditions must be met: “An informed, high-level official of the U.S. government has determined that the targeted individual poses an imminent threat of violent attack against the United States; (2) capture is infeasible, and the United States continues to monitor whether capture becomes feasible, and (3) the operation would be conducted in a manner consistent with applicable law of war principles.”

The white paper, however, spells out rules under which such attacks can be ordered that appear to be much less stringent that what administration officials have said.

It says, for example, that the United States isn’t required “to have clear evidence that a specific attack on U.S. persons and interests will take place in the immediate future.”

It also says the United States has the right under international law to act under the suspicion that an attack might take place.

“It must be right that states are able to act in self-defense in circumstances where there is evidence of further imminent attacks by terrorist groups even if there is no specific evidence of where such an attack will take place or of the precise nature of the attack,” it says. “Delaying action . . . would create an unacceptably high risk that the action would fail and that American casualties would result.”

Several experts called that an exaggerated rewrite of the legal definition of “imminence,” something that the administration has labeled “elongated imminence.”

The three Americans killed under the program all died in drone strikes in Yemen in 2011. They were Anwar al Awlaki, a New Mexico native Obama administration officials claim was the operations chief of al Qaida’s Arabian Peninsula branch; Samir Khan, an Islamist writer who grew up in New York City and whose family now lives in North Carolina, and Awlaki’s teenage son, Abdulrahman, who was born in Colorado. The elder Awlaki and Khan were killed on Sept. 30, 2011; the younger Awlaki died in a separate drone strike two weeks later.

Jonathan S. Landay contributed to this report.