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Hard conflicts sometimes need the soft touch of truth. That could now be the case for the two Koreas, which have been at odds for 70 years, either in all-out war or frequent violent encounters.

On Sept. 25, in a rare admission of fallibility, the “supreme leader” of North Korea apologized to the South Korean people. Kim Jong Un wrote in a letter that he was sorry for his military shooting a South Korean official found floating in the sea a few days earlier.

He also admitted the killing “will clearly” have a negative impact on inter-Korean relations. In the spirit of reconciliation, Mr. Kim promised such incidents would not recur.

Was his apology sincere? Or merely a self-serving charm offensive to split South Korea from its ally, the United States, which is deeply concerned about North Korea’s nuclear arsenal?

At the least, his apparent contrition lies in contrast to a similar incident in 2008, when a South Korean tourist was killed after straying into a North Korean military area. Mr. Kim’s father, Kim Jong Il and ruler at the time, did not apologize.

In addition to the apology, this third member of the Kim family to rule seems to be chafing under the aura of infallible leadership handed down in the propaganda machine set up by his grandfather, Kim Il Sung. (As part of the dynasty’s deification, all North Koreans must wear lapel pins with images of the late Kims.)

As with many leaders who rely on a personality cult, the humility to admit mistakes is often seen as a weakness – and dangerous. Yet in August, Mr. Kim told his people that his 2016 economic plan had failed due in part to his government’s “shortcomings.” In a country where it is a crime to criticize policy, Mr. Kim’s honest self-reflection could open a door for others to do so.

Last March, Mr. Kim told propaganda workers to move away from the “mystification” of him and focus more on his “human” side. If the people are mesmerized by a leader, he wrote, that might cover up the truth.

Three days after Mr. Kim’s apology, South Korean President Moon Jae-in followed suit. He apologized to his own people for his government’s failure to protect the citizen killed by North Korea. He said Mr. Kim’s apology opens an opportunity for dialogue. He proposed the two countries jointly investigate the incident.

Small gestures like an apology can often turn around a broken relationship. They hint that someone is willing to change. They help break down stereotypes of “the other” and point to a shared reality of truth and even affection. The Koreas have a long path to a permanent peace. Yet when leaders come off their false pedestals, it can set peace in motion.