"A letter was sent by President Trump and correspondence between the two leaders has been ongoing," White House press secretary Sarah Huckabee Sanders said.
North Korean state media first reported that Kim received a personal letter from Trump. Kim said the letter "is of excellent content," according to the Korean Central News Agency.
Additional details about what was in the dispatch were not provided.
"Kim Jong Un said that he would seriously contemplate the interesting content," the state news agency reported.
Secretary of State Mike Pompeo said the U.S. and North Korea were in a "better place" and expressed hope that working level talks with North Korea can begin.
"I'm hopeful that this will provide a good foundation for us to begin to continue these important discussions with the North Koreans to denuclearize the peninsula," Pompeo said.
News of the letter comes as Trump prepares to depart for the G-20 summit in Japan next weekend, where he is expected to hold talks with Chinese President Xi Jinping.
China is one of North Korea's few allies.
Trump has walked a controversial line in his relationship with Kim, at times expressing affection for the North Korean dictator while at other times threatening Pyongyang if it does not comply with his demands.
Last month, the North test fired missiles, which Trump's national security advisor John Bolton said violated a U.N. Security Council resolution.
But Trump had largely downplayed those tests and expressed confidence that the U.S. and North Korea will reach a deal on its nuclear program.
At the time, Trump said he believed Kim would do nothing to interfere with the "great economic potential" of North Korea.
"He also knows that I am with him & does not want to break his promise to me," Trump said of Kim.
Trump has held two summits with the North Korean leader, first in Singapore and then in Vietnam. The February summit in Vietnam, however, abruptly ended without an agreement when the North demanded an end to sanctions and Trump reportedly passed a note to Kim demanding that he turn over his nukes.
In April, the North also said it tested a new tactical guided weapon. The test came less than two months after the failed Vietnam summit and was the first public weapons test by the North since the historic Singapore summit.