That would mark the first such outreach from North Korea, which backed out of a potential meeting with Vice President Pence at the Winter Olympics in South Korea last month. North Korea has vowed it will not give up its nuclear weapons, but the United States insists that any negotiations to lower tensions would have the goal of denuclearization.
It was not clear whether Trump was describing a direct conversation or messages sent through diplomatic channels. Trump has previously said he thinks he could have a good relationship with Kim, were they ever to try to resolve tensions directly. A U.S. official said earlier this year that Trump and Kim had never spoken.
North Korea greatly accelerated its testing of ballistic missiles last year and claims it can deliver a nuclear weapon anywhere in the United States. U.S. officials dispute the claim but acknowledge North Korea possesses intercontinental ballistic missiles.
Trump has vowed not to repeat what he calls the mistakes of past administrations that negotiated with North Korea. Talks never stopped North Korea from pursuing weapons and left the United States looking weak, Trump has said. He said last year that Secretary of State Rex Tillerson was wasting his time trying to open talks, but he has more recently said he would consider them under the right conditions.
Trump has not laid out how any future negotiations would be structured, except to say that North Korea's nuclear weapons must be on the table.
Trump spoke Saturday at a press dinner, where some of his remarks were in jest.
“I would not rule out direct talks with Kim Jong Un,” Trump said in a lighthearted tone. “I just won't. As far as the risk of dealing with a madman is concerned, that's his problem, not mine,” he said to laughter. “He must be a fine man.”
Turning serious, Trump also said the United States “saved the Olympics” by taking a hard line on North Korea. South Korea, the host of the games, credits Trump's “strong attitude” for North Korea's attendance, he said.
“That's true, whether people want to hear it,” Trump said at the Gridiron Club dinner. “And they had a very successful Olympics. That was heading for disaster.”