The secretary, speaking alongside South Korean Defense Minister Song Young-Moo, added that North Korea has carried out “reckless, outlaw behavior,” and that the United States and South Korea “are serious about solving this problem.”

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Mattis visited the Demilitarized Zone that separates the two countries after months of provocations by the North Korean military, including the launch of a ballistic missile over Japan and an underground nuclear test Sept. 3. North Korean leader Kim Jong Un’s regime has threatened to carry out a hydrogen bomb test over the Pacific, an even more striking event that would grab worldwide attention.

Senior U.S. officials have raised concerns about North Korea for decades, but the recent provocations — and clear signs that the Kim regime is making progress in its goal to build an intercontinental ballistic missile capable of carrying a nuclear warhead — have put world leaders on edge.

The standoff grew increasingly tense as Kim and President Trump exchanged a series of insults and threats over the summer. Trump threatened to rain “fire and fury” upon Pyongyang if it continues to threaten the United States and taunted Kim as “Rocket Man.” Kim’s regime threatened to fire missiles toward the U.S. Pacific territory of Guam before ultimately deciding in August not to do so.

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The rhetoric has cooled since, but U.S. officials and their allies, especially in South Korea and Japan, continue to watch North Korea closely. After a flurry of military activity this year, the regime has not carried out a missile test since Sept. 15. However, it is broadly accepted that another test could occur at any time.

Mattis is in Seoul for a meeting Saturday with senior South Korean defense officials, and arrived as Marine Gen. Joseph F. Dunford Jr., chairman of the Joint Chiefs of Staff, also was in South Korea to meet with his counterparts. Dunford will travel next to Hawaii for a three-party meeting that will include his South Korean counterpart, Gen. Jeong Kyeong-doo, and their Japanese equivalent, Adm. Katsutoshi Kawano.

Trump is expected to visit the country in November, an event whose preparations are being closely watched here.

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The United States and its allies are widely seen as having few options to deal with Pyongyang’s behavior. North Korea has thousands of artillery pieces aimed across the border at Seoul, a city of about 10 million people, and Mattis has warned that direct conflict would be catastrophic.