North Korean leader Kim Jong Un and South Korean President Moon Jae-in kicked off their third meeting on Tuesday, during which Kim said his “historic” summit with U.S. President Donald Trump in June had improved regional stability and raised hopes for further progress.

A joint statement expected from the two leaders at the conclusion of their talks on Wednesday will provide clues to whether negotiations between North Korea and the United States over dismantling Pyongyang’s nuclear programs could regain momentum.

The outcome will also be a litmus test for another meeting Kim has recently proposed to Trump.

Kim pledged to work toward the “complete denuclearisation of the Korean peninsula” during his first meeting with Moon in the Demilitarised Zone that separates the two Koreas in April, and at his summit with Trump in June.

But discussions over how to implement the vague commitments have since faltered, with Washington demanding concrete action toward denuclearization by North Korea before agreeing to a key goal of Pyongyang - declaring an end to the 1950-53 Korean War.

Pyongyang has given no indication it is willing to give up its nuclear arsenal unilaterally and is seeking relief from tough international sanctions.

U.S. State Department spokeswoman Heather Nauert told a news briefing on Tuesday that Washington hoped the latest North-South summit would bring about “meaningful, verifiable steps toward the denuclearization of North Korea” and called it a “historic opportunity” for Kim to follow through on commitments he made at his June summit with Trump.

Nauert said the United States would “continue to consult very closely and carefully and regularly with the South Koreans” during their meetings in North Korea.

This week’s summit, the third between Kim and Moon this year, is intended to craft concrete steps to implement the Panmunjom Declaration, named after the border village where they first met, Seoul officials said.

The two Koreas are also working to adopt a separate military accord aimed at defusing tensions and preventing armed clashes between the old foes, which are technically still at war because the 1950-1953 Korean War ended with a truce, not a peace treaty.

The neighbors have already agreed to withdraw some guard posts and equipment, in a bid to transform the world’s most heavily fortified border into a no-weapons area.

“What we’re trying to achieve is irreversible, lasting peace. We want to move towards a new era based on the existing agreement, not a new declaration,” Moon’s press secretary Yoon Young-chan told a news briefing on Tuesday.

According to aides to Moon, Trump has asked Moon to be “chief negotiator” between himself and Kim, after the U.S. president canceled a trip to Pyongyang by Secretary of State Mike Pompeo last month citing lack of progress in nuclear talks.

The United States is pressing countries to strictly observe U.N. sanctions aimed at choking off funding for Pyongyang’s nuclear and ballistic missile programs, which are a threat to the United States.

This will be a likely theme when Pompeo hosts a meeting of the U.N. Security Council on North Korea on Sept. 27 on the sidelines of the annual U.N. General Assembly.

Traveling with Moon in North Korea are South Korean business tycoons, who met North Korean Deputy Prime Minister Ri Ryong Nam, who is in charge of economic affairs on Tuesday. Seoul officials said they did not expect any specific joint economic projects to be agreed given international sanctions.

Pyongyang says it has destroyed its main nuclear and missile engine test site, and has halted atomic and ballistic missile tests, but U.S. officials and analysts believe it is continuing to work on its weapons plans clandestinely.

South Korea is pinning high hopes on Kim’s remarks to Moon’s special envoys earlier this month that he wanted to achieve denuclearization within Trump’s first term in office ending in early 2021, although Kim at the same time stressed that Washington must reciprocate his initial “goodwill” gestures.

“While Moon has expressed his desire to agree on a concrete plan on denuclearization, we believe that the two nations still differ on this concept,” said Anwita Basu, an analyst at the Economist Intelligence Unit.

In previous, failed talks, North Korea has said it could consider giving up its nuclear program if the United States provided security guarantees by removing troops from South Korea and withdrawing its so-called nuclear umbrella of deterrence from the South and Japan.

U.S. officials involved in the latest negotiations have said North Korea has refused to even start discussions about defining denuclearization.

“Overall, the third inter-Korean summit will probably have the most concrete outcome and will set the tone for any future summits between Kim and Trump,” said Basu.

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