The letter released by Mr. Trump is filled with flowery language, but it makes no mention of nuclear weapons or any intention by the North to give them up.

“I deeply appreciate the energetic and extraordinary efforts made by Your Excellency Mr. President for the improvement of relations between the two countries and the faithful implementation of the joint statement,” it said.

In another sign of tensions that belied the public pleasantries exchanged by Mr. Kim and Mr. Trump, the United States complained to a United Nations sanctions panel this week about what the Trump administration has described as rampant violations of the severe limits on North Korean imports of refined petroleum.

United Nations Security Council diplomats said the United States had submitted evidence to the panel that suggested the North Koreans had furtively imported nearly 1.4 million barrels of refined petroleum this year, roughly triple the permitted amount for 2018.

The evidence, from a declassified United States intelligence briefing seen by The New York Times, said the petroleum had been smuggled into North Korea via illicit ship-to-ship transfers at sea. The briefing said it had information that suggested such transfers had been carried out at least 89 times between January and May.

The American complaint, first reported by The Wall Street Journal, asked the sanctions panel to “order an immediate halt to all transfers of refined petroleum products to the D.P.R.K.”

The complaint singled out China and Russia, which have continued to sell refined petroleum to North Korea and historically have resisted the use of sanctions as a pressure tactic.