NEW DELHI—U.S. Defense Secretary Robert Gates said al Qaeda is working with an array of local militant groups to destabilize South Asia and trigger a war between India and Pakistan, an indication of growing U.S. fears about new terror attacks throughout the volatile region.

Mr. Gates said al Qaeda had formed alliances with the Afghan and Pakistani Taliban as well as with Lashkar-e-Taiba, a Pakistani-based group that carried out the attacks in Mumbai in 2008 that left more than 160 dead.

The...