President Trump became the first sitting U.S. president to step inside North Korea—a “great honor,” he said—part of an impromptu meeting with the isolated regime’s leader Kim Jong Un at the demilitarized zone that divides the two Koreas.

After meeting at the boundary Sunday afternoon, the two leaders walked a short distance into the North, stopped for photographs, and then walked back. This time Mr. Kim broke the barrier, crossing into the South. Surrounded by reporters, aides and security personnel, the men stood shoulder-to-shoulder and spoke for a few minutes.

They then unexpectedly walked into the “Freedom House” building on the South Korean side. Mr. Kim sat down with Mr. Trump and answered several questions, saying he had been surprised by the U.S. request to meet.

“We can change in a positive way from now on,” Mr. Kim said, noting their meeting spot—the truce village of Panmunjom—carried historical significance as a symbol of the Korean Peninsula’s division and sad history.

Expected to be brief—handshakes and a brief hello—the get-together stretched past 15 minutes before Messrs. Trump and Kim left for a closed-door meeting.

The surreal sequence of events underscored the unconventional detente between the U.S. and North Korea, long-time adversaries whose leaders have struck a warm personal connection. The prelude to Sunday’s meeting was a bout of letter writing that Mr. Trump called “beautiful” and Mr. Kim described as “excellent.”

“Good to see you again,” Mr. Kim said as they stood face-to-face at the border. He then told Mr. Trump he would be the first U.S. president to cross over and Mr. Trump did so, at 3:46 p.m. local time, patting his counterpart on the shoulder as he stepped over a small concrete curb. The two walked just under 20 steps into the North.

“Stepping across that line was a great honor,” Mr. Trump later recalled. Asked if he would invite Mr. Kim to the U.S., he answered: “I would invite him right now.”

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