Trump did not divulge what was in the letter from Kim.
Still, Trump offered compliments to the dictator, calling their relationship "very strong" and describing Kim as "quite a guy and quite a character". "That's very important to me", Trump said.
North Korea's state media has not mentioned any letter. Their second summit in Vietnam in February broke down because of the distance between the two leaders' positions over the North Korean nuclear arsenal, but Trump stressed that it was not the end of negotiations.
The latest USA allegation comes after a report by a UN Panel of Experts submitted to the council earlier this year that said North Korea successfully evaded sanctions to import as much as seven-and-a-half times the allowed amount of refined petroleum last year.
That, according to the Wall Street Journal report, would have limited his value as a source of intelligence.
The two sides haven't held working-level talks in months and North Korea hasn't responded to multiple requests to restart the negotiations, according to US officials.
According to Singapore's foreign ministry, North Korea's embassy there had been planning an event to commemorate the summit anniversary and invited Singapore officials, but later cancelled the event. But it later canceled the event.
In the message to Putin, Kim called the April summit a "significant and important occasion that made a honest and good close relationship between ourselves and opened a new history" of the North Korea-Russia friendship.
According to the Journal, the person said Kim Jong Nam had traveled to Malaysia in February 2017 to meet his Central Intelligence Agency contact, although that may not have been the sole objective of the trip.
Bolton said the United States was continuing its "maximum pressure campaign" because Kim still appeared not to have made "a strategic decision to give up the pursuit of deliverable nuclear weapons".
Trump's remarks to reporters on the South Lawn of the White House represented a fresh attempt by the president to cozy up to the North Korean leader, a policy that has drawn criticism for seeming to overlook Kim's autocratic rule. Trump even said the unlikely pair "fell in love" over the correspondence.
"If the period of no dialog is prolonged, the passion for dialog could subside", Moon said during a visit to Oslo.
Susan Rice, who was national security adviser for Trump's Democratic predecessor, Barack Obama, tweeted her reaction: "America, this tells you all you need to know about our so-called 'Commander-in-Chief'".
Lee joined her husband's 2000 trip to Pyongyang for the summit and also visited the North Korean capital in 2011 after the death of Kim Jong Il, when she met and expressed her condolences to Kim Jong Un.
"We're looking, of course, to build a lasting peace".
More than half of those surveyed in the United States and Japan believed that sanctions should be employed alongside dialogue in dealing with North Korea. It interviewed 1,000 citizens in the United States, China, Japan and Russian Federation for two weeks from the last week of May.
Early optimism that the leaders' personal rapport would lead to a deal on denuclearisation weakened after their most recent talks ended without an agreement and competing accounts of why the summit ended in disarray.
"It is an intricate and complex problem and can not be solved overnight", Geng told reporters.
In May, North Korea twice tested multiple short-range missiles, which analysts said could be aimed at penetrating South Korea's missile defence system.