The U.S. moved forcefully to try to counter China's bid for influence over increasingly jittery Asian neighbors by sending a pair of B-52 bombers over disputed islands in the East China Sea, U.S. officials said Tuesday.

The B-52s took off from Andersen Air Force Base in Guam and flew more than 1,500 miles northwest, crossing into what China has declared as its new air-defense identification zone, at about 7 p.m. ET Monday. The U.S. deliberately violated rules set by China by refusing to inform Beijing about the flight, officials...