The talks took place in Mexico, where the two were attending the inauguration ceremony of President Andres Manuel Lopez Obrador on Saturday.
Kang also had a brief meeting with Senior White House Adviser Ivanka Trump, the minister added.
READ MORE: South Korea Mulls Boosting Support to North Korea Defectors — Ministry
The situation on the Korean Peninsula has improved since the beginning of this year as North Korean leader Kim Jong-un engaged in a dialogue with his South Korean counterpart President Moon Jae-in and Trump. During the landmark Kim-Trump summit in June, the two leaders agreed that Pyongyang would make efforts toward denuclearization in exchange for the freeze of US-South Korean military drills as well as the potential removal of US sanctions.