"We really established a very good relationship," Trump said at a White House Cabinet meeting. "We'll probably have another meeting."
Trump's comments came one day after Kim warned the current goodwill with the U.S. could end if Washington continues to impose sanctions to force his government to denuclearize.
North Korean leader Kim Jong Un poses for photos in Pyongyang in this Jan. 1, 2019, photo released by North Korea's Korean Central News Agency (KCNA).
In his annual New Year's Day address, Kim said it was his "firm will" that North Korea will no longer produce or test nuclear weapons, or "use or spread" its arsenal. Kim added he was prepared to hold another meeting with U.S. President Donald Trump this year. But he said his country may have to follow another path unless Washington takes "corresponding measures." Kim called on the U.S. and South Korea to end all joint military drills.
Kim and Trump signed a vaguely worded agreement during their historic summit in Singapore last June, but further negotiations have stalled in part over Pyongyang's opposition to Washington's call for complete denuclearization prior to granting any concessions.
People watch a TV news on a screen showing North Korean leader Kim Jong Un delivering a New Year's speech, at Seoul Railway Station in Seoul, South Korea, Jan. 1, 2019.
North Korea is also demanding that the U.S. and South Korea first issue a peace declaration to formally end hostilities and replace the armistice that has been in effect since the Korean War ended in 1953. Critics worry a peace declaration could undermine the justification for the U.S. military presence in South Korea.
Despite Kim's warning, South Korea's Unification Ministry welcomed his address, saying it reflected Kim's commitment toward complete denuclearization and lasting peace on the Korean peninsula, and the continued improvement of inter-Korean relations.
Tuesday's speech was delivered exactly one year after Kim announced his willingness to send a contingent of North Korean athletes to the Winter Olympics in Pyeongchang, South Korea the following month. The speech set off a series of diplomatic breakthroughs, including three summits with South Korean President Moon Jae-in and the meeting with President Trump.