SEOUL, South Korea — The United States and South Korea wrapped up their annual joint military exercises on Thursday by flying some of their most powerful warplanes in bombing drills in a show of force two days after North Korea fired a ballistic missile over Japan.

Two B-1B supersonic bombers and four F-35 stealth fighter jets from the United States Air Force and Marine Corps joined four South Korean F-15 fighter jets in live-fire bombing exercises over a military range in eastern South Korea, officials said.

On their way to join the South Korean jets, the American warplanes flew together with two F-15s from Japan’s Self-Defense Forces over waters near the southwestern Japanese island of Kyushu, the United States Pacific Command said in a statement.

”This complex mission clearly demonstrates our solidarity with our allies and underscores the broadening cooperation to defend against this common regional threat,” said Gen. Terrence J. O’Shaughnessy, commander of the United States Pacific Air Forces, referring to North Korea.