News of the meeting was delivered by South Korean officials after talks with Mr. Trump at the White House, the BBC reports.
They passed a verbal message from Mr. Kim, saying the North Korean leader was “committed to denuclearisation.”
South Korea’s President, Moon Jae-in, said the news “came like a miracle.”
“If President Trump and Chairman Kim meet following an inter-Korean summit, complete denuclearisation of the Korean peninsula will be put on the right track in earnest,” he said.
China has welcomed the development, saying the Korean peninsula issue was “heading in the right direction” and calling for “political courage.”
However, the BBC says the North has halted missile and nuclear tests during previous talks, only to resume them when it lost patience or felt it was not getting what it demanded.
The latest announcement came days after the South Korean delegation met Mr. Kim in Pyongyang.
Speaking outside the White House after briefing Mr. Trump, South Korean National Security Adviser, Chung Eui-yong, said he had passed on a message that Mr. Kim was “committed to denuclearisation” and had “pledged that North Korea will refrain from any further nuclear or missile tests.”