Photo/IllutrationNorth Korean leader Kim Jong Un, right, meets with South Korean National Security Director Chung Eui-yong in Pyongyang on Sept. 5. (South Korea Presidential Blue House/Yonhap via AP)

SEOUL--South Korean President Moon Jae-in said Friday that he's pushing for "irrevocable progress" on efforts to rid North Korea of its nukes by the end of this year as he prepares for his third summit with North Korean leader Kim Jong Un.

Earlier this week, Moon sent special envoys to Pyongyang to help resolve the nuclear stalemate. After returning home, his envoys said Thursday that Kim still has faith in U.S. President Donald Trump and reaffirmed his commitment to a nuclear-free Korean Peninsula though Kim expressed frustration over outside skepticism about his sincerity.

Trump later responded by tweeting, "Kim Jong Un of North Korea proclaims 'unwavering faith in President Trump.' Thank you to Chairman Kim. We will get it done together!" Moon said the outcome of his envoys' Pyongyang trip was "much more than what was expected."

The next step in nuclear diplomacy is uncertain. Negotiators seem deadlocked over whether North Korea truly intends to denuclearize as it has pledged numerous times in recent months. North Korea has dismantled its nuclear and rocket engine testing sites, but U.S. officials want more serious, concrete action taken before North Korea obtains outside concessions.

While meeting the South Korean envoys, Kim said he's willing to take stronger steps if his "goodwill" measures are met in kind, according to chief South Korean envoy Chung Eui-yong. Kim has repeatedly said he wants a step-by-step disarmament process, where each of his actions is reciprocated with corresponding outside concessions.

North Korea, which says its nuclear program is aimed at countering U.S. military threats, has demanded the United States jointly declare the end the 1950-53 Korean War, which ended with an armistice not a peace treaty. During his meeting with the South Korean envoys, Kim said an end-of-war declaration wouldn't weaken the U.S.-South Korean alliance or lead to the withdrawal of the 28,500 U.S. troops stationed in South Korea to prevent a North Korean attack, according to Chung.

Moon's liberal government, which is keen on continuing engagement with the North, also wants the declaration. In a written interview released Friday with Indonesian newspaper Kompas, Moon said he wants to see such a declaration made this year as part of trust-building measures.

"What matters is implementing with sincerity the agreements among the leaders, and our objective is producing irrevocable progress by the end of this year," Moon said, referring to denuclearization and a permanent peace on the Korean Peninsula.

During the Seoul envoys' trip, the two Koreas agreed Kim and Moon would meet in Pyongyang from Sept. 18-20, in their third summit since April. South Korean officials say the summit will focus on how to achieve the denuclearization of the Korean Peninsula.