BEIJING — South Korea wants to discuss unease about an American antimissile system on its soil. Taiwan is eager to buy weapons. The Philippines hopes to find out whether the United States plans to challenge China in the South China Sea.

Leaders across Asia are looking to Washington for guidance on a variety of pressing diplomatic issues.

But President Trump’s erratic approach to policy making and his focus on one issue — North Korea’s nuclear weapons program — are creating anxiety and confusion in the region.

In South Korea, Mr. Trump has angered the public with several remarks, including his suggestion that the country, an ally for over six decades, pay for an antimissile system built by the Americans to deter North Korea. Moon Jae-in, who was elected president on Tuesday, has vowed to seek a more conciliatory approach with the North, setting up a potential rift with American policy.