Trump talked to reporters after escorting Kim out of the Oval Office and posing for photos, along with Pompeo, before Kim's departure. "It went very well", President Trump told reporters on the White House lawn.
"I want it to be very meaningful", he said.
In the latest sign of hostility cooling down but hopes kept in check, Trump said he's unilaterally put a hold on new sanctions against the North "until the talks break down".
South Korea says building trust with North Korea is crucial amid a USA -led diplomatic push to persuade the North to give up its nuclear weapons.
Trump referred to the letter from Pyongyang as "interesting".
Vietnam hails Trump-Kim summit
Rodman also traveled to Singapore for the diplomatic talks , which his agent, Darren Prince, previously confirmed to CNN . One of them, Foal Eagle, involves field maneuvers, with about 11,500 USA troops and 290,000 South Koreans participating.
"Come to Russia, we'll be very happy to see you", Lavrov told Kim in remarks released by the Russian foreign ministry.
Plans for the high-stakes sit-down in Singapore had been cast into doubt. Responding to a question, Trump said he had never cancelled the meeting. "We welcome the summits that already took place between Pyongyang and Seoul as well as planned meetings between North Korean and USA leadership".
"I look forward to the day I can take the sanctions off North Korea", Trump said.
Since taking power in 2011, Kim has not publicly met with another head of state in North Korea.
Trump has refused to publicly acknowledge whether he's spoken directly with Kim Jong Un ahead of the talks.
Société: Un randonneur meurt en croyant manger du coscoll
Un retraité français de 78 ans est décédé vendredi soir après avoir consommé cette plante hautement toxique. Il est nécessaire de demander à un spécialiste avant d'utiliser la plante pour la cuisine.
"We're meeting with the chairman on June 12, and I think it's probably going to be a very successful - ultimately, a successful process".
The US secretary of state, who spoke with Mr Trump on Wednesday night and with National Security Adviser John Bolton early on Thursday, was accompanied by Andrew Kim, the head of a Central Intelligence Agency unit assigned to work on North Korea, and Mark Lambert, the head of the State Department's Korea desk.
If held, the Trump-Kim meeting would be the first summit between the two countries that have always been at odds over the North's pursuit of nuclear weapons and ballistic missiles capable of striking the U.S.
Trump said countries in the region - Japan and South Korea - were also involved in this.
Les aides sociales coûtent un "pognon de dingue" selon Macron — Pauvreté
"On met un pognon de dingue dans les minima sociaux et les gens ne s'en sortent pas", s'exclame le président de la République. Emmanuel Macron aborde ensuite le reste à charge zéro: "C'est dans ce contexte-là qu'on fait le reste à charge zéro ".
U.S. officials with knowledge of the letter's contents said it did not make any noteworthy threats or concessions, and was seen as a positive gesture. He also expressed Moscow's support for an agreement Kim reached with South Korean President Moon Jae-in at a summit last month that focused on measures to ease hostilities and increase exchanges between the two Koreas.