Although no official details of the content of the letter have been released, Kim praised Trump's "extraordinary courage".
Trump made the remarks during an interview with the Washington-based political newspaper The Hill when asked about the letter that he recently received from Kim.
The White House confirmed the existence of the letter in an email to Reuters news agency.
Trump leaves for Asia later this week for the G20 summit in Osaka, Japan, and meetings with South Korean President Moon Jae-in Seoul.
Nuclear negotiations have been at a standstill since then, but on the eve of the anniversary of their Singapore summit in June past year, Trump told U.S. reporters he received a "beautiful" letter from Kim, without revealing what was written.
North Korea is seeking a step-by-step approach in which moves toward denuclearisation are matched by concessions from the United States, notably a relaxation of the sanctions.
The official didn't confirm whether Trump will be visiting the demilitarized zone (DMZ), a trip that was thwarted during the US president's previous trip to Seoul in 2017. The U.S. President Trump "is reviewing" an option to visit the DMZ during his two-day stay in South Korea later this week, the official said.
Apple reportedly canceled quantum dot camera technology for the iPhone 11
Recent reports indicated that the iPhone XR successor will have a bigger battery compared to the one found in the iPhone XR. This means it is likely to sell for less than #$1,000 when it is released, the Business Insider noted.
Mike Pompeo to hold talks with NSA Ajit Doval
The US reaction on the contentious deal came hours before US Secretary of State Mike Pompeo's arrival in India. While US delinked both issues, India will continue to pursue the matter of tightening of H1B visa rules.
Hornets' Kemba Walker to Celtics as Kyrie Irving's replacement?
The team already traded Aron Baynes and may go into next season with a very young team led by Jayson Tatum and Jaylen Brown. Free Agency begins on June 30th at 6:00 PM ET.
Analysts say the gesture of sending letters is part of North Korean efforts to present Kim as a legitimate global statesman who is reasonable and capable of negotiating solutions and making deals.
'I'm hopeful that this will provide a good foundation for us to begin. these important discussions with the North Koreans, ' Pompeo told reporters.
However, perceived leniency from South Korea and the USA may give Kim Jong Un more confidence that he can get away with provocative and escalatory behavior, which may lead to further military exercises if Kim's meetings with key world leaders occurring ahead of the G20 Summit do not go as planned.
'I think we're in a better place, ' Pompeo said.
Both leaders responded positively to each other's letter, planting hope that there may be a break in the deadlocked talks.
The US has insisted North Korea quit its nuclear programme while Pyongyang has demanded sanctions support.
North Korea has been reluctant to hold working-level talks and Kim prefers to deal with Trump directly.
The North Korean leader told the Chinese president that his visit was an opportunity to demonstrate "the immutability and invincibility of the DPRK-China friendship before the world", KCNA said, using the abbreviation of North Korea's official name. North Korea's nuclear program is not the only topic on the Trump-Moon summit agenda. North Korea has called the complex "the heart" of its nuclear program, while many outside experts say it's an aging facility and that North Korea is believed to have additional multiple secret uranium enrichment facilities.