WASHINGTON—The Central Intelligence Agency is preparing to launch a secret program to kill al Qaeda militants in Yemen, where months of antigovernment protests, an armed revolt and the attempted assassination of the president have left a power vacuum, U.S. officials say.

The covert program that would give the U.S. greater latitude than the current military campaign is the latest step to combat the growing threat from al Qaeda's outpost in Yemen, which has been the source of several attempted attacks on the U.S. and is home...