SEOUL—Former United Nations Secretary-General Ban Ki-moon abruptly dropped his plans to pursue the presidency of South Korea, leaving the country’s ruling conservatives without a clear candidate to succeed impeached President Park Geun-hye.

Mr. Ban’s exit on Wednesday paves the way for the ascension of rival Moon Jae-in, a candidate who has called for closer ties with North Korea, the rethinking of a U.S.-backed missile-defense system in South Korea, and a tougher line on sprawling conglomerates such as Samsung and Hyundai.

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