WASHINGTON — The Obama administration’s secret legal memorandum that opened the door to the killing of Anwar al-Awlaki, the American-born radical Muslim cleric hiding in Yemen, found that it would be lawful only if it were not feasible to take him alive, according to people who have read the document.

The memo, written last year, followed months of extensive interagency deliberations and offers a glimpse into the legal debate that led to one of the most significant decisions made by President Obama — to move ahead with the killing of an American citizen without a trial.

The secret document provided the justification for acting despite an executive order banning assassinations, a federal law against murder, protections in the Bill of Rights and various strictures of the international laws of war, according to people familiar with the analysis. The memo, however, was narrowly drawn to the specifics of Mr. Awlaki’s case and did not establish a broad new legal doctrine to permit the targeted killing of any Americans believed to pose a terrorist threat.

The Obama administration has refused to acknowledge or discuss its role in the drone strike that killed Mr. Awlaki last month and that technically remains a covert operation. The government has also resisted growing calls that it provide a detailed public explanation of why officials deemed it lawful to kill an American citizen, setting a precedent that scholars, rights activists and others say has raised concerns about the rule of law and civil liberties.