A sticking point for some skeptics was whether any mission that included firing missiles from drone aircraft could be portrayed as not amounting to hostilities.

As the May 20 deadline approached, Mr. Johnson advocated stopping the drone strikes as a way to bolster the view that the remaining activities in support of NATO allies were not subject to the deadline, officials said. But Mr. Obama ultimately decided that there was no legal requirement to change anything about the military mission.

The administration followed an unusual process in developing its position. Traditionally, the Office of Legal Counsel solicits views from different agencies and then decides what the best interpretation of the law is. The attorney general or the president can overrule its views, but rarely do.

In this case, however, Ms. Krass was asked to submit the Office of Legal Counsel’s thoughts in a less formal way to the White House, along with the views of lawyers at other agencies. After several meetings and phone calls, the rival legal analyses were submitted to Mr. Obama, who is a constitutional lawyer, and he made the decision.

A senior administration official, who spoke on the condition of anonymity to talk about the internal deliberations, said the process was “legitimate” because “everyone knew at the end of the day this was a decision the president had to make” and the competing views were given a full airing before Mr. Obama.

The theory Mr. Obama embraced holds that American forces have not been in “hostilities” as envisioned by the War Powers Resolution at least since early April, when NATO took over the responsibility for the no-fly zone and the United States shifted to a supporting role providing refueling assistance and surveillance — although remotely piloted American drones are still periodically firing missiles.

The administration has also emphasized that there are no troops on the ground, that Libyan forces are unable to fire at them meaningfully and that the military mission is constrained from escalating by a United Nations Security Council resolution.