While it has been widely reported that the United State carried out the strikes, the Obama administration has never officially acknowledged responsibility for them. The New York Times has described the details of a secret Justice Department memorandum that concluded that it would be lawful to target Anwar al-Awlaki if capturing him was infeasible. The Times and the A.C.L.U. have sued for disclosure of that document under the Freedom of Information Act.

Several administration officials, including Attorney General Eric H. Holder Jr. in a speech at Northwestern University in March, have also defended the targeting of citizens, without a trial, if they join terrorist groups and under certain conditions.

“Some have argued that the president is required to get permission from a federal court before taking action against a United States citizen who is a senior operational leader of Al Qaeda or associated forces,” Mr. Holder said. “This is simply not accurate. ‘Due process’ and ‘judicial process’ are not one and the same, particularly when it comes to national security. The Constitution guarantees due process, not judicial process.”

In 2010, reports surfaced that Anwar al-Awlaki had been placed on a “kill list” after the attempted bombing of a Detroit-bound airliner on Dec. 25, 2009. The would-be bomber is said to have told his interrogators that Mr. Awlaki recruited him for the operation. Mr. Awlaki has also been accused of playing a role in other terrorist plots, but he was not indicted or tried.

The complaint says Mr. Awlaki should not have been designated “for death without the protections of a judicial trial” by the executive branch and contends that at the time of his killing, he did not present any immediate “concrete, specific and imminent threat of death or serious bodily injury.” It also asserts that any threat he did present when he was found could have been mitigated without lethal force, although it does not say how.

Complicating matters, it is believed that the Sept. 30 strike specifically targeted Anwar al-Awlaki, making the people around him — including Mr. Khan — collateral damage. Likewise, Mr. Awlaki’s son is said to have been a bystander in the Oct. 14 strike. Mr. Khan was involved in producing propaganda for Al Qaeda’s Yemen branch, but Abdulrahman al-Awlaki had not been accused of joining the group.

Under the international laws of war, civilians may not be deliberately targeted; while it can sometimes be lawful to shoot at a military target knowing that some civilians nearby may be killed, collateral deaths must be minimized and proportional to the military objective. Still, it is not clear how domestic-law constitutional rights interact with wartime targeting law, and the A.C.L.U. and the Center for Constitutional Rights dispute the extent to which armed-conflict rules apply in Yemen. In discussing Mr. Khan and Abdulrahman al-Awlaki, the complaint accuses the defendants of failing to take adequate measures to prevent bystanders from harm.

“Even in the context of an armed conflict, government officials must comply with the requirements of distinction and proportionality and take all feasible measures to protect bystanders,” it says.