President Moon Jae-in says North Korean leader Kim Jong-un hopes to hold his second summit with U.S. President Donald Trump as soon as possible for swifter progress on denuclearization. 

The South Korean president relayed the North Korean leader's stance during a press briefing in Seoul on Thursday, after returning from trip to the North for his third summit with Kim. 

Moon said Kim also expressed hope that U.S. State Secretary Mike Pompeo will soon make another trip to the North. 

Moon assessed that the regime has changed significantly on denuclearization, noting its earnest discussions with the South on specific related measures. 

The president said he and Kim shared the perception that the current North-U.S. dialogue is not going smooth and that advancing talks between Pyongyang and Washington is closely connected to the development of inter-Korean relations. 

He said the North also requested the South to mediate North Korea-U.S. dialogue and continue close cooperation for complete denuclearization. 

Moon said they had many conversations about denuclearization and relations between the North and the U.S. He said Kim told him that he wants to complete denuclearization at an early date so he can instead focus on economic development. 

Kim also expressed the will to permanently dismantle the North's nuclear program if the U.S. follows through with the agreements reached during its first-ever summit with the North in June and take “corresponding measures” in line with what the North is doing. 

Moon said he hope the U.S. will put itself in the North’s shoes, to recognize the regime’s will and stance, and quickly resume dialogue with Pyongyang, adding that this latest inter-Korean summit has created the conditions for the resumption of those talks. 

During the summit, the two sides also agreed to hold parliamentary talks and enhance exchanges between local governments. 

Moon wrapped up his three-day trip to North Korea with a visit to Mount Baekdu before getting on the Seoul-bound Air Force Two at Samjiyon Airport near the mountain. 

The airplane arrived at Seoul Air Base in Seongnam, Gyeonggi Province, at around 5:40 p.m., about two hours and 10 minutes after takeoff.