“A letter was sent by President Trump and correspondence between the two leaders has been ongoing,” White House spokeswoman Sarah Sanders said in an email.
Earlier North Korea's state-run news agency KCNA said Kim would put serious thought into the content of the letter, details of which it did not describe.
The KCNA report said Kim described the letter as being "of excellent content" and that he "would seriously contemplate the interesting content."
U.S.-North Korea talks stalled after a failed summit in February between Trump and the North Korean leader in Hanoi, Vietnam.
A U.S. official said on Wednesday the United States had no pre-conditions for new talks, but that progress would require meaningful and verifiable North Korean steps to abandon its nuclear weapons program.Trump leaves for Asia later this week for the G20 summit in Osaka, Japan, and meetings with South Korean President Moon Jae-in Seoul.