In recent months, United States and British Special Operations teams have increased clandestine reconnaissance missions in Libya to identify the militant leaders and map out their networks for possible strikes. Military planners are still awaiting orders on whether American involvement would include striking senior leaders, attacking a broader set of targets, or deploying teams of commandos to work with Libyan fighters who promise to support a new Libyan government. Any military action would be coordinated with European allies, officials said.

Teams of American Special Operations forces have over the past year been trying to court Libyan allies who might join a new government in a fight against the Islamic State, also known as ISIS or ISIL.

But commanders say they are dealing with a patchwork of Libyan militias that remain unreliable, unaccountable, poorly organized and divided by region and tribe.

“How long will the United States and the Europeans wait until they say, we have to work with whatever militias we can on the ground?” said Frederic Wehrey, a Libya specialist at the Carnegie Endowment for International Peace, who frequently visits the country.

In a meeting of his National Security Council last Thursday to discuss escalating the fight against the Islamic State, Mr. Obama asked his advisers to prepare whatever military measures were necessary to combat the militants in Libya while not undercutting the international effort to help form a national unity government.

For the president, the challenge is to avoid embarking on yet another major counterterrorism campaign in his last year in office while also moving decisively to prevent the rise of a new arm of the Islamic State that if left unchecked analysts say could attack the West, including Americans or American interests.