SEOUL, South Korea >> South Korean President Moon Jae-in said today he is pushing for “irrevocable progress” in efforts to rid North Korea of its nuclear weapons by the end of this year as he prepares for his third summit with North Korean leader Kim Jong Un.

Meanwhile, U.S. President Donald Trump said he was expecting to get a “positive” letter from Kim after South Korean special envoys traveled to Pyongyang this week to help resolve the nuclear stalemate and pave the way for the Sept. 18-20 Moon-Kim summit.

South Korean officials say the summit in Pyongyang will focus on how to achieve denuclearization of the Korean Peninsula — the goal that Kim and Trump agreed to at their own historic face-to-face meeting in Singapore in June. Diplomatic progress since then has been slow.

After returning home from North Korea, the South Korean envoys said Thursday that Kim still has faith in Trump and reaffirmed his commitment to a nuclear-free Korean Peninsula, although he expressed frustration over skepticism about his sincerity. Chief envoy Chung Eui-yong said Kim wanted to denuclearize before Trump’s current term ends in early 2021.

On today, Trump was upbeat about the North Korean leader’s overtures, describing as “a very positive statement what he said about me and also what he said about he wants to denuclearize during the Trump administration.”

Trump said he’s expecting to get a letter in the coming days that Kim is sending to him through Secretary of State Mike Pompeo. It was a reference to the message from Kim to Trump that South Korea said Thursday it would be forwarding to the United States. During their visit on Wednesday, the envoys had forwarded a message from Trump to Kim.

“I know that a letter is being delivered to me, a personal letter from Kim Jong Un to me,” Trump told reporters aboard Air Force One as he traveled to a campaign event in North Dakota. “I think it’s going to be a positive letter.”

Still, 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.

North Korea, which says its nuclear program is aimed at countering U.S. military threats, has demanded the United States jointly declare with that country and South Korea an end to the 1950-53 Korean War, which was halted by 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 an North Korean attack, according to Chung.

Kim’s stance appeared designed to allay U.S. concerns that the declaration could be used by the North to demand the removal of U.S. forces.

Moon’s liberal government, which is eager to continue engagement with North Korea, also wants the declaration. In a written interview released today 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.

Two senior members of South Korea’s delegation to Pyongyang are to fly to China and Japan to brief them on their meeting with Kim. Chung is to meet senior Chinese official Yang Jiechi on Saturday, and National Intelligence Service director Suh Hoon, who went to Pyongyang with Chung, is to meet Japanese Prime Minister Shinzo Abe on Monday, according to South Korea’s presidential office.

Chung, whose official title is presidential national security director, spoke with his U.S. counterpart, John Bolton, on the phone on Thursday about his trip to North Korea.