"We're getting along very well".
As reported by the Atlantic, rapidly improving relations between the North and South over the past year are a good indication that the conflict, which has spanned almost 70 years since the initiation of hostilities in 1950 may finally be coming to an end.
Trump recently said he is likely to hold a second summit with Kim in January or February.
However, North Korea has taken steps to cease its ballistic missile and nuclear programs.
North Korea is seeking security guarantees from the US and relief from worldwide sanctions.
In a speech past year, South Korean President Moon Jae-in said he dreamt of building a railroad connecting the divided neighbours.
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After Trump and Kim met in June in Singapore, negotiations between Washington and Pyongyang have been stuck due to bilateral differences on key problems over the scale of denuclearisation, U.S. sanctions, and whether to issue a war-ending declaration, among others.
Pence has also said it was essential that worldwide sanctions pressure be maintained on North Korea until its complete denuclearisation was achieved.
Last November, a North Korean soldier was critically wounded in a jointly controlled area after he fled to the South amid a hail of bullets fired by his former comrades.
They have also begun work to reconnect a train line and fix another rail link across the border. The South Koreans have expressed hope the visit - which would be a first for a North Korean leader - could happen by the end of this year. "We have a good relationship", Trump told reporters aboard Air Force One on his return from the G20 summit.
Kim and Trump pledged at their first meeting to work towards denuclearisation, although the two sides have since made little progress agreeing on a timeline or concrete steps.