The general has said that the trip is meant to offer transparency to America’s allies in the region and to prevent any miscalculation on China’s part about the Pentagon’s intentions. He arrived in China on Monday night, and will travel to Japan later in the week.

South Koreans, many living within range of North Korean artillery, were particularly alarmed by Mr. Trump’s threat to bring down “fire and fury” on the North if Pyongyang continued to threaten the United States with nuclear missiles.

On his way to Seoul, General Dunford said his trip was in support of Mr. Tillerson’s diplomatic and economic campaign to deter North Korea. Even as Mr. Trump has issued one provocative statement after another against the North, Mr. Tillerson has been reminding Pyongyang that the door to dialogue is open if the nation halts missile and nuclear tests.

“As a military leader, I have to make sure that the president does have viable military options in the event that the diplomatic and economic pressurization campaign fails,” General Dunford told reporters on his plane. “But even as we develop those options, we are mindful of the consequences of those options, and that gives us a greater sense of urgency to make sure we are doing everything we absolutely can to support Secretary Tillerson’s path.”

The general’s calibrated statement appeared to be an attempt to calm allies in South Korea while backing up Mr. Trump’s warnings to the North.

Concern escalated in the Trump administration about the North’s nuclear threat after the country flight-tested two intercontinental ballistic missiles last month, the second of which appeared to have the capacity to reach the American mainland. It is not clear that the North can accurately target such a missile or build a nuclear warhead that can survive re-entry into the atmosphere.