“At this time” signals this document is partly a negotiating tactic — to win a meeting later, after a period of North Korean silence.

Therefore, please let this letter serve to represent that the Singapore summit, for the good of both parties, but to the detriment of the world, will not take place. You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used.

This is a return to the my-button-is-bigger-than-your-button rhetoric that typified the early days of relations between Mr. Trump and Mr. Kim.

I felt a wonderful dialogue was building up between you and me, and ultimately, it is only that dialogue that matters. Some day, I look very much forward to meeting you.

A “wonderful dialogue,” but the administration says there has been no direct contact between the two leaders — their exchanges have been through South Korean delegations, President Moon Jae-in of South Korea and Mr. Pompeo.

In the meantime, I want to thank you for the release of the hostages who are now home with their families. That was a beautiful gesture and was very much appreciated.

This acknowledges Mr. Kim’s humanitarian gesture — and makes no mention of the thousands of Koreans in North Korean gulags.

If you change your mind having to do with this most important summit, please do not hesitate to call me or write.

Here Mr. Trump is putting the ball in Mr. Kim’s court.

The world, and North Korea in particular, has lost a great opportunity for lasting peace and great prosperity and wealth. This missed opportunity is a truly sad moment in history.

The president portrays himself here as the spurned peacemaker, and places the blame squarely on Mr. Kim. “Great prosperity and wealth” harkens back to the motive that Mr. Trump believes drives his fellow leaders.