U.S. President Donald Trump and North Korean leader Kim Jong Un extended warm invitations to one another on Sunday, exchanging lofty visions for the future as they met at the Demilitarized Zone (DMZ) separating the two Koreas.

The leaders shook hands on the North Korean side of the DMZ, making Trump the first sitting American president to ever set foot in the hermit state, before crossing together to the South Korean side and shaking hands again.

"It's a great honor to be here," Trump said, adding, "I feel great." Upon leaving closed-door talks with Kim, he described the meeting as "very, very good."

Kim said this was "an expression of his willingness" to work toward a new future.

While the two spoke of reconciliation and diplomatic progress, Trump said that U.S. sanctions on the country over its nuclear weapons and missile development programs would stay for now. The leaders agreed to designate a team to work out the details of future negotiations, Trump said, adding that the U.S. team would be headed by Washington's nuclear envoy Stephen Biegun and that work would begin "over the next two or three weeks."

The sticking point between the historical adversaries has long been the issue of denuclearization, a term whose definition the two countries can't seem to agree on. Washington wants Pyongyang to give up its nuclear weapons, while Kim and his predecessors view the term to mean broader concessions from the U.S., including the removal of its troops from the Korean peninsula.