Not only has Mr. Moon steered two headstrong, erratic adversaries away from a military conflict that could have been devastating for his nation, he has maneuvered the Trump administration into pursuing negotiations that it has long resisted — but that he and his allies on South Korea’s political left have long pressed for.

And he will set the stage for any meeting between Mr. Trump and Mr. Kim when he first sits down with the North Korean leader for a summit meeting next month in the Demilitarized Zone.