SEOUL—The U.S. sent four of its most advanced jet fighters and a pair of B-1B bombers over the Korean Peninsula, alongside Japanese and South Korean jets, as a show of force in direct response to North Korea firing a missile over Japan.

The flyover Thursday, which included a bombing drill on a range in South Korea, came at the end of annual joint U.S.-South Korean military exercises that have angered Pyongyang.

It...