WASHINGTON—The foiled mail bombing plot by suspected al Qaeda militants in Yemen has added urgency to an Obama administration review of expanded military options that include putting elite U.S. hunter-killer teams that operate secretly in the country under Central Intelligence Agency authority.

Officials said support was growing both within the military and the administration for shifting more operational control to the CIA—a move that would allow the U.S. to strike suspected terrorist targets unilaterally with greater stealth...