These developments, combined with a surprise meeting Saturday between Kim and South Korea's president, Moon Jae-in, rekindled hopes of progress toward halting the North's nuclear weapons program.
Unlike the previous summit in April, which had been planned in advance and included ceremonial elements and press facilities for some 3,000 journalists from across the world, today's summit took place with no forewarning.
In a letter sent to the North Korean dictator on Thursday, Mr Trump said the meeting on June 12 would be called off "based on tremendous anger and open hostility" shown by Pyongyang.
In a tweet, Trump the summit was "likely" to happen as scheduled June 12.
It was South Korean officials who first informed the United States earlier this year that Mr Kim was prepared to discuss potential nuclear disarmament.
"We will neither beg the USA for dialogue nor take the trouble to persuade them if they do not want to sit together with us", she said. "We'd like to do it".
-North Korea summit a success, the presidential Blue House said.
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"We would like to make known to the USA side once again that we have the intent to sit with the USA side to solve problem regardless of ways at any time", Kim Kye Gwan, a vice foreign minister, said in a statement carried by the country's official media on Friday.
"Moon Jae-in is acting decisively to keep his people safe from war", said Adam Mount, a nuclear expert at the Federation of American Scientists.
But North Korean state media, in a measured response, stated that they were still open to meeting the U.S. president.
President Moon's spokesman said there had been a "candid" exchange of views in the two hours of talks between the two leaders.
Pompeo past year assembled a working group at the Central Intelligence Agency called the Korea Mission Center, which gradually assumed the lead role in talks with the North Koreans, and the group's director, a retired senior Central Intelligence Agency official with deep experience in the region, became the main US interlocutor with Pyongyang.
North Korea has conducted six nuclear tests since 2006 and numerous tests of intercontinental ballistic missiles that could, theoretically, reach the US. Kim wants to make a "grandiose proposal", he said, such as denuclearization in exchange for normalizing relations, but agreeing to that without working out the finer points could have serious ripple effects, including taking away the legal justification for USA troops on the peninsula.
Asked Friday if the North Koreans were playing games with their communications, Trump responded: "Everybody plays games. And, as a number of us have been saying all along, the most you can hope for out of any meeting is a statement of general principles that will guide future negotiations", said Wit, who also negotiated with the North Koreans while serving with the State Department.
Early this month, North Korea cancelled a high-level meeting with Seoul over South Korea's participation in regular military exercises with the United States and insisted that it will not return to talks unless its grievances are resolved.