The "denuclearization" of the Korean Peninsula now appears more of a bilateral affair between the two Koreas without the participation of the United States and its unpredictable president.

North Korean dictator Kim Jong-un hinted as much when he recently received a South Korean delegation that called on him and handed him a letter from South Korean President Moon Jae-in. Kim is said to have responded warmly upon reading Moon's letter, which was delivered by Chung Eui-yong, Moon's national security adviser.

North Korean state media said Kim praised Moon's letter as commendable. It also said Kim wanted to relay to Moon North Korea's intention to de-escalate the existing and tense situation on the Peninsula as soon as possible. In addition, Kim gave South Korea permission to open an inter-Korea liaison office in Kaesong, North Korea, which is the site of a joint economic zone.

Political observers have taken Kim's remarks to mean Kim remains keen on denuclearization but apparently on his terms. North Korea's definition of denuclearization is one involving the dismantling of the United States' nuclear umbrella defending South Korea and the withdrawal of all U.S. military forces from South Korea.

North Korean state media said Kim made the remarks and showed his appreciation for Moon on Wednesday, shortly after meeting with the five-member delegation. Following this meeting, the state-owned KCNA news agency added further details to the talks.

It said Kim is committed to step-by-step denuclearization, which means a process extending over an unspecified period of time. Kim made no mention of involving the U.S. in these new talks.

Kim also showed gratitude to Moon for his letter, said KCNA. Kim is said to have expressed his gratitude for Moon's appraisal of the new progress in North-South relations. He also urged both countries to overcome the many challenges ahead while opening a bright future for both countries "through a steadfast will."

Moon and Kim will get another chance to get the denuclearization talks back on track - and possibly involve the Americans - when they meet at an Inter-Korean Summit from Sept. 18 to 20. This will be the third meeting between both leaders since April.

Moon's trip to North Korea will be the first visit by a South Korean head of state since 2007. The leaders are expected to take a bold step towards declaring an end to the Korean War and finally signing a peace treaty to end this war that ended in an Armistice on July 27, 1953.