That has made him the first US President to visit our country.
North Korea has publicly called for an end to the crippling economic sanctions imposed by the United States and the United Nations.
He added: "We met and we liked each other from day one and that was very important", Trump said.
New White House press secretary Stephanie Grisham today showed she will fight for freedom of the press, getting into a brawl with North Korean security guards. Trump warned that if war broke out, he would rain "fire and fury" on North Korea.
The meeting dominated the pages of the official Rodong Sinmun newspaper on Monday.
Addressing thousands at St. Peter's Square in Italy's Vatican City, Francis said he "salute [d]" Trump and Kim for taking the step to meet. However, Trump's private talks with Kim lasted about 50 minutes, turning into an impromptu summit. "I think the fourth US-North Korea summit is possible within this year".
The Korean Central News Agency reports that the two leaders expressed great satisfaction over the results of their talks.
The first Trump-Kim summit took place in a blaze of publicity in Singapore previous year but produced only a vaguely worded pledge about denuclearisation. Then they met in Hanoi, Vietnam in February, but talks broke down without any joint agreement as Kim pushed for sanctions relief and the USA pushed for denuclearisation. This time, instead of discussing specific measures, the two leaders focused only on atmosphere.
Lee Sang-min, spokesman of South Korea's Unification Ministry, said that the Trump-Kim meeting could breathe new life into the nuclear negotiations and benefit Seoul's efforts to keep alive momentum for talks and cooperation with the North.
Such a trip would have to come "at the right time", he added.
"It's just an honor to be with you and it was an honor that you asked me to step over that line", Trump told the North Korean leader.