The White House said in a statement on Saturday after Trump's meeting with the Chinese president, Xi Jinping, that they and Kim would strive "to see a nuclear free Korean Peninsula".
Before the division of the Korean peninsula in 1948, there were two railway lines linking the North to the South - one in the west and the other in the east. "Related agencies plan to investigate him regarding the details of how he came to the South".
In 2012, a North Korean soldier walked unchecked through rows of electrified fencing and surveillance cameras, prompting Seoul to sack three field commanders for the security lapse.
More than 30,000 North Koreans have fled to the South since the 1950-53 war on the peninsula ended in an armistice instead of a peace treaty.
South Korean and U.S. soldiers stand guard at the truce village of Panmunjom, July 2017.
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He was a World War Two aviator and Texan oil tycoon before entering politics in 1964 as a Republican. In a letter to his wife on January 6, 1994, Mr Bush said she had given him "joy that few men know".
"We're getting along very well".
Trump told reporters aboard Air Force One on his return from Argentina he thinks the meeting will be in early 2019.
A North Korean soldier reportedly defected to South Korea at around 7:56 a.m. local time on Saturday.
The Trump-Kim summit in June of this year was created to help ease the tensions between the two nations - though critics have questioned whether North Korea has complied with agreements reached at the historic meeting. The line was cut in November 2008 due to political tensions over North Korea's nuclear program and the hard-line policies of a new conservative government in Seoul.
They also had to get special one-off clearance from the United Nations to get around sanctions, which prohibit taking fuel and certain equipment into North Korea.
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The first Trump-Kim summit took place in June in Singapore but Trump has said the next meeting will probably take place at a new location.
They have also begun work to reconnect a train line and fix another rail link across the border.
Earlier on Friday, while meeting with his South Korean counterpart Moon Jae-in, Trump discussed his intention to hold a second U.S. -DPRK summit, and restated with Moon a common commitment to work closely together on making it happen. The inspections are preparations for a project to connect the railways of the Koreas, as agreed between leaders of the South and North at their summits this year.
Furthermore, he said he would be interested in inviting Kim to the US for talks at "some point" in the future.
Seoul plans to hold a groundbreaking ceremony before the end of the year on a plan to establish road and rail links between the two Koreas, first agreed upon by the countries' two leaders at a summit in April.
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