U.S. and Yemeni officials have agreed to restart a controversial military-training program to help the new president tackle emboldened al Qaeda militants, as part of planned enhanced counterterrorism relationship.

While President Abdu Rabu Mansour Hadi has openly turned to Washington as he attempts to get the upper hand over the terrorist group, his policy may have a key drawback: upsetting the delicate political balance of power in the country and complicating the sensitive task of overhauling the nation's fractured security...