"What's most important now is that there must not be even the slightest vacuum in state affairs," Han said in a nationally televised address from the government complex in Seoul.
Han became acting president after parliament voted to impeach Yoon earlier in the day.
"I deeply feel the responsibility for the current circumstances facing our citizens and the process that led us here," he said.
The veteran technocrat promised to maintain South Korea's security posture and international relationships.
"We will maintain our strong security readiness and carefully manage our external trust," he said. "The entire Cabinet will do its utmost to maintain trust with the U.S., Japan, and our other allies."
Speaking at an emergency Cabinet meeting earlier in the day, Han urged civil servants to remain focused on their duties. "The most important mission at this moment is to quickly stabilize any confusion in state affairs and return precious daily life to our citizens," he said.
Han cited South Korea's resilience through past crises, including the 1997 financial crisis and COVID-19 pandemic.
"Our country has emerged stronger from numerous challenges," he said. "We will ensure stable governance strictly according to the constitution and law."
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