WASHINGTON — The Central Intelligence Agency is building a secret air base in the Middle East to serve as a launching pad for strikes in Yemen using armed drones, an American official said Tuesday.

The construction of the base is a sign that the Obama administration is planning an extended war in Yemen against an affiliate of Al Qaeda that has repeatedly tried to carry out terrorist plots against the United States.

The clandestine American operations in Yemen are currently being run by the military’s Joint Special Operations Command, with the C.I.A.’s assistance and with the approval of Yemen’s fragile authoritarian government.

But with Yemen’s embattled government on the brink of collapse, Obama administration officials are concerned that a future government might not support American operations. By putting the operations under C.I.A. control, they could be carried out as a “covert action,” which can be undertaken without the support of the host government.