WASHINGTON, Sept. 5 (Yonhap) -- An improvement in inter-Korean ties must be accompanied by progress toward dismantling North Korea's nuclear weapons program, the United States said Wednesday in response to a South Korean special envoy's meeting with North Korean leader Kim Jong-un.

The meeting took place in Pyongyang the same day as the two sides seek to arrange a third summit between South Korean President Moon Jae-in and Kim later this month.

Chung Eui-yong, Moon's top national security adviser, returned to Seoul late Wednesday with his delegation, and the outcome of the trip will be released Thursday.

"As President Moon has stated, 'The improvement of relations between North and South Korea cannot advance separately from resolving North Korea's nuclear program," a State Department spokesperson said in response to a Yonhap query.

"We reaffirmed the Panmunjom Declaration during the Singapore Summit and we did so because progress on inter-Korean relations must happen in lockstep with progress on denuclearization," the official added.

Moon and Kim adopted the Panmunjom Declaration after their first summit in April, pledging to improve cross-border ties and pursue "complete denuclearization" of the Korean Peninsula.

At the June summit between U.S. President Donald Trump and Kim, the leaders reaffirmed that declaration as North Korea again committed to "work towards complete denuclearization of the Korean Peninsula" in exchange for security guarantees from the U.S.

But denuclearization talks between Washington and Pyongyang have since stalled amid an apparent difference in their interpretation of the summit deal.

And last month, Trump canceled a planned trip to Pyongyang by U.S. Secretary of State Mike Pompeo, citing a lack of progress in denuclearization efforts.

Source: Yonhap News Agency