Still, administration officials acknowledge that the sudden threat from ISIS to Americans — several of whom are still held by the militants in Syria — had complicated the calculus for the United States in a conflict Mr. Obama has largely avoided.

“There are a lot of cross pressures here in this situation,” the White House press secretary, Josh Earnest, told reporters. “There’s no doubt about that. But our policy as it relates to pursuing American interests in this region of the world are actually really clear, that we want to make sure that we are safeguarding American personnel.”

Under plans being developed by the administration, a senior official said, the United States could target leaders of the militant group in and around their stronghold, the northern city of Raqqa, as well as in isolated outposts to the east, near the Iraqi border.

While the Syrian government has the capability to partly defend its airspace from American warplanes, American fighter jets can fly close to the border and fire on targets in Syria using long-range precision weapons.

The American military could also jam Syria’s air-defense systems by sending signals that would make it difficult or impossible for radar to pick up American fighter planes entering Syrian airspace. Such a move would give fighters a limited amount of time to hit ISIS targets or camps before leaving Syria. The military could also use B-2 stealth bombers, which are almost invisible to radar, or could fire at stationary targets in Syria using Tomahawk cruise missiles, launched from ships at sea.

On Monday, even as he warned the Obama administration against unilateral strikes in Syria, Walid Muallem, the foreign minister, said, “Syria is ready for cooperation and coordination at the regional and international level to fight terrorism.” Mr. Assad has long tried to rally support by portraying the insurgency against him as a terrorist threat. He has made little headway with the West or his Arab neighbors.

Syria’s strategy, some former administration officials say, carries a risk for the United States, particularly if the moderate opposition is squeezed out by ISIS.