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 is the first time the F-35B jets have been used in such a mission with the B-1B bombers over the peninsula, the U.S. Air Force Pacific Command said in a statement. It said the flyover—which also included two Japanese F-15 and four South Korean F-15K jet fighters—emphasized an “ironclad commitment” to the defense of allies and the U.S., and maintained a readiness to give leaders “viable and ready military options.”

The latest move threatens to raise the temperature again on the peninsula, after North Korea’s launch Tuesday of an intermediate-range ballistic missile that soared over the Japanese city of Hakodate and landed in the Pacific Ocean.

The U.S. said Thursday’s mission was in direct response to North Korea’s missile launch.

“North Korea’s actions are a threat to our allies, partners and homeland, and their destabilizing actions will be met accordingly,” said Gen. Terrence J. O’Shaughnessy, Commander of the Pacific Air Forces. “Our forward-deployed force will be the first to the fight, ready to deliver a lethal response at a moment’s notice if our nation calls.”

North Korea’s state media, in a statement Thursday, called the flyover a reflection of the “bellicose nature” of the U.S. and South Korea’s military drill, and said that it showed how threatened the U.S. felt after the North’s Tuesday missile launch over Japan.

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“The wild military acts of the enemies are nothing but the rash act of those taken aback by the intermediate-to-long range strategic ballistic rocket launching drill conducted by the army of the DPRK as the first military operation in the Pacific,” the Korean Central News Agency wrote.

In Washington, Defense Secretary Jim Mattis said the U.S. is still engaged in diplomacy, which he defined to include economic sanctions and other measures and not limited to actual talks. The U.S. is seeking newer and tougher sanctions to use against North Korea while pressuring other countries and businesses to cut off ties with Pyongyang. “Are we out of diplomatic options? No, we’re not,” Mr. Mattis said.

He also said he and President Donald Trump were not at odds earlier in the week when Mr. Mattis called for diplomacy after Mr. Trump tweeted a message about North Korea that said, “Talking is not the answer!”

Meantime, the top U.S. general in South Korea rapped Pyongyang for having responded to what he described as reduced U.S.-South Korean military drills—which he said he hoped “would send a positive signal to North Korea”—with more provocations.

“Apparently the changes in the exercise did not matter,” Gen. Vincent Brooks said in a statement.

Earlier this month, North Korea threatened to surround the U.S. Pacific territory of Guam with “enveloping fire” by launching four intermediate-range missiles into the waters around the island.

The threat came after Pyongyang complained about previous American B-1B flyovers and warned the U.S. against conducting further such exercises.

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Days later, Pyongyang said that leader Kim Jong Un had decided against firing missiles toward Guam for now, but that he would continue to watch the U.S.’s behavior during the joint military exercises. The U.S. and South Korea say the maneuvers are defensive in nature, but the North regards them as a precursor to invasion.

On Aug. 20, the day before the exercises began, Rodong Sinmun, North Korea’s main party newspaper, warned that its military was “keeping a high alert” and would “take resolute steps the moment even a slight sign of the ‘preventive war’ is spotted.”

North Korea says the U.S. is considering a unilateral strike against it, while President Trump said earlier this month that military options were “locked and loaded.”

North Korea has threatened Guam, in particular, because of the presence of the Andersen Air Force base there, from which the U.S. has launched a number of B-1B flyovers of the Korean Peninsula this year in response to Pyongyang’s missile tests.

In Thursday’s flyover mission, the two B-1B bombers were from the Andersen base and the four F-35B jets were from Marine Corps Air Station Iwakuni in Japan, according to the U.S. Pacific Command.

In a statement carried Wednesday by state-run Korean Central News Agency, Mr. Kim called Tuesday’s missile launch over Japan a “meaningful prelude to containing Guam.”

On the same day, after the launch, South Korea sent four of its jet fighters to simulate a bombing raid aimed at destroying “the enemy’s leadership.”

Meanwhile, Japan’s defense ministry Thursday sought approval to bolster the country’s missile-defense capability. The budget request includes radar that can quickly locate North Korea’s submarine-launched missiles, and weapons to shoot down projectiles at high altitudes.

Thursday’s flyover included two B-1B bombers from the Guam Air Force base, four F-35B jet fighters the Marine Corps Air Station in Iwakuni, Japan, two F-15Js from the Japanese air force and four South Korean F-15K jet fighters, according to U.S. Pacific Command.

During the 10-hour mission, the F-35Bs, B-1Bs and Japanese F-15s flew together over Japanese waters before the U.S. planes joined the South Korean fighters to practice “attack procedures” in South Korea, it said.

Write to Jonathan Cheng at jonathan.cheng@wsj.com