Halting the drone strikes would appear contrary to Houthi interests, since the chief U.S. target, Al Qaeda in the Arabian Peninsula, or AQAP, is the Houthis’ archenemy. The two groups have clashed repeatedly in recent days, including an AQAP attack on a Houthi-controlled hospital Sept. 28 that killed 15 people.

Yet the new era of multi-sided Middle Eastern conflicts has brought “the death of the idea that the enemy of my enemy is my friend,” said the State Department official, who asked for anonymity to discuss internal assessments. “It seems not to work that way anymore.”

Rep. Adam B. Schiff (D-Burbank), a member of the House Intelligence Committee, said in an interview that he worries that the crisis in Yemen might lead to a government collapse that “could only enhance AQAP’s ability to control ground and launch terror attacks.”