SEOUL, South Korea -- The United States on Thursday flew some of its most advanced warplanes over South Korea in a show of force against North Korea, after Pyongyang fired a midrange ballistic missile over Japan earlier this week, South Korea's military said.

Two U.S. B-1B bombers and four F-35 fighters participated in training with South Korean F-15 fighter jets, an official from Seoul's Defense Ministry said.

The planes took part in bombing exercises in a military field near South Korea's eastern coast, but it wasn't immediately clear whether they were live-fire drills, according to the official. The B-1Bs were flown in from Andersen Air Force Base in Guam while the F-35s came from a U.S. base in Iwakuni, Japan, the official said. He didn't want to be named, citing office rules.

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Such flyovers are common when animosity rises on the Korean Peninsula, which is technically in a state of war because the 1950-53 Korean War ended with an armistice, not a peace treaty.

CBS News correspondent Ben Tracy says that while the U.S warplanes did not cross into North Korean airspace, the message of the maneuvers was clear. The show of force came just hours after the U.S. conducted a missile defense test off the coast of Hawaii, launching a ballistic missile and then shooting it out of the sky.

A medium-range ballistic missile target is launched from the Pacific Missile Range Facility on Kauai, Hawaii, during what the U.S. Missile Defense Agency said was a "complex missile defense flight test" on Aug. 29, 2017. The target was successfully intercepted by SM-6 missiles fired from the USS John Paul Jones. MDA/Handout

North Korea on Tuesday flew a potentially-nuclear capable Hwasong-12 intermediate range ballistic missile over northern Japan and later called it a "meaningful prelude" to containing the U.S. territory of Guam.

Pyongyang had earlier threatened to fire a salvo of Hwasong-12s toward Guam, which is home to key U.S. military bases and strategic long-range bombers the North finds threatening.

The U.S. has been talking to North Korea, and paying them extortion money, for 25 years. Talking is not the answer! — Donald J. Trump (@realDonaldTrump) August 30, 2017

But with the standoff escalating, there are conflicting messages from Washington on how to handle the Kim regime.

On Wednesday, President Trump appeared to signal that he had given up on diplomatic efforts to ease the standoff with North Korea, tweeting that, "talking is not the answer!"

Hours later, however, Mr. Trump's Secretary of Defense James Mattis contradicted that, saying at the Pentagon, in direct response to a question about his boss's remarks: "No. We're never out of diplomatic solutions. We always look for more. We're never complacent."

Tracy notes that Thursday is the final day of the joint U.S.-South Korea military exercises, which the North views as rehearsals for an invasion.

That could offer an opportunity for things to cool off in the region, but North Korea has called the launch of its missile over Japan merely a "curtain raiser," and Kim has ordered his military to launch more missiles into the Pacific.