HONG KONG — The meeting between North Korea’s leader, Kim Jong-un, and President Moon Jae-in of South Korea offered a rare opportunity to hear Mr. Kim speak spontaneously, without the filter of his nation’s state news media.

While much of the discussion between the two leaders was not revealed, South Korean officials did describe some. These are among their comments during Friday’s meeting on the South Korean side of the Demilitarized Zone.

“Now you are here in the South, and I wonder when I can cross over to the North,” Mr. Moon said when Mr. Kim crossed the border and they shook hands. “Why don’t you now?” Mr. Kim said.

He took Mr. Moon by the hand and they crossed over a low concrete slab that marks the border. They stood in North Korea, shaking hands for a few seconds, before returning to the South.

Mr. Kim found a moment to make light of his country’s missile and nuclear tests, which have caused such deep concern in recent years.

“I heard you had your early-morning sleep disturbed many times because you had to attend the N.S.C. meetings because of us,” Mr. Kim said with a smile, referring to the security council. “Getting up early in the morning must have become a habit for you. I will make sure that your morning sleep won’t be disturbed.” “Now I can sleep in peace,” Mr. Moon replied.

In one conversation, Mr. Kim made reference to several delicate points in relations between the two sides.

“On my way here I saw that those who had been nervous about any shelling from the North Korean Army — including the Yeonpyeong Island residents, North Korean defectors and displaced people — do have high hopes for our meeting today,” he said.

Mr. Kim’s mention of Yeonpyeong Island refers to a 2010 attack from the North that killed two South Korean marines and two civilian construction workers. The “displaced people” is a reference to Korean families who were separated during the Korean War.

“I look forward to making the most of this opportunity so that we have the chance to heal the wounds between the North and the South,” Mr. Kim added. “The demarcation line, which is in fact not high, may disappear with many people stepping on it and passing over it.”

Mr. Moon mentioned a recent bus crash in North Korea that killed 32 Chinese tourists and four North Korean workers.