Moon was elected in a landslide in May after campaigning on promises to reach out to North Korea. He has shown a willingness to take a harder line in recent months following a series of ballistic missile tests by Pyongyang, including two that indicated it has developed intercontinental ballistic missiles capable of reaching the U.S. mainland.
He faces domestic political pressure to tamp down Trump's unpredictable and bellicose pronouncements, which have set many South Koreans on edge.
Trump's threat to "totally destroy" North Korea if the U.S. or its allies had to defend itself from an attack, delivered in front of the United Nations General Assembly in September, rattled some politicians in Seoul, who fear Trump is pushing for a military attack on North Korea's nuclear program and has ruled out diplomatic options.
South Korea's top diplomat reflected that unease Monday, calling for a peaceful solution during an interview in Seoul with NBC News' Lester Holt.
"Another war on the Korean Peninsula must not happen," South Korea's Foreign Minister Kang Kyung-wha said. "A resolution to the North Korean nuclear issue must be pursued in a peaceful, diplomatic manner."
(Special correspondent Matt Stiles in Seoul contributed to this report.)
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