SEOUL—The U.S. flew two B-1B bombers and four F-35 stealth fighters over the Korean Peninsula, in a show of force ahead of the United Nations General Assembly where world leaders will discuss how to contain North Korea’s nuclear ambitions.

Monday’s exercise, which followed one on Aug. 31, was in direct response to North Korea’s launch of a missile over Japan last week, the U.S. Pacific Command said in a statement. Earlier this month Pyongyang carried out its sixth nuclear test, its most powerful so far, defying international...