WASHINGTON — It has become a favorite parlor trick of President Trump’s, and on Wednesday, he was at it again, brandishing his latest letter from the North Korean dictator, Kim Jong-un.

“Those few people that I’ve shown this letter to,” Mr. Trump told reporters during a cabinet meeting, his voice trailing off as he waved three typewritten sheets in front of the cameras. “They’ve never written letters like that. This is a great letter. We’ve made a lot of progress with North Korea and Kim Jong-un.”

If history is any guide, he will end up showing Mr. Kim’s letter to more than a few people. Mr. Trump delights in sharing with visitors the correspondence he has received from North Korea’s leader since they began writing to each other last year.

Typically, according to people who have witnessed such displays, Mr. Trump calls to an assistant sitting just outside the Oval Office to bring him “the letters,” which he then fans out across the Resolute Desk so the people facing him can get a glimpse. They are translated into English and filled with flowery references to Mr. Trump as “Your Excellency.”