During that meeting, leaders will also address the destruction of a missile-testing facility in North Korea, which was first brought up during the summit in Singapore.
The ministry added: "We had expected that the USA side would offer constructive measures that would help build trust based on the spirit of the leaders' summit. we were also thinking about providing reciprocal measures".
The statement was sure to fuel growing skepticism in the USA and elsewhere over how serious Kim is about giving up his nuclear arsenal.
The top USA diplomat continued to describe his conversations with senior North Korean officials as "productive", even as North Korea attacked the US negotiating stance.
"We agreed to the denuclearization of North Korea", Trump said.
"These are complicated issues but we made progress on nearly all of the central issues".
"The US attitude and positions at the high-level talks on Friday and Saturday were extremely regrettable", the North's Foreign Ministry said in a statement, the South's Yonhap reported.
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Brazil , Belgium , France and Uruguay will hold news conferences ahead of their respective quarter-final meetings on Friday. The hosts continued their remarkable run by knocking out tournament favorites Spain on penalties.
U.S. Secretary of State Mike Pompeo ended his latest trip to North Korea on Saturday without meeting leader Kim Jong-un and trailed by accusations of "gangster-like" arm-twisting from a newly emboldened regime.
The statement claimed the two countries' gestures of goodwill since the summit were lopsided in their significance, comparing North Korea's "irreversible step" of dismantling its nuclear test site with the American move to suspend military exercises, "which can be resumed any time at any moment".
"If those requests were gangster-like, the world is a gangster", says US Secretary of State Mike Pompeo, noting that numerous UNSC resolutions have demanded the North rid itself of nuclear weapons and end its ballistic missile programme.
A Pentagon team would be meeting with North Korean officials around 12 July at the border between North and South Korea to discuss the repatriation of remains, Mr Pompeo told reporters.
After he met Japanese Minister of Foreign Affairs Taro Kono, Pompeo said he was in Tokyo to discuss the USA alliance with Japan and maintaining "maximum pressure" on North Korea, an expression Trump's administration had backed away from after the Singapore summit. "But this expectation and hope of ours were so naive as to be gullible". "The North Koreans understand that and have not challenged that".
The administration worked for months to win China's support for its "maximum pressure" campaign of sanctions to isolate North Korea, which does most of its global trade with the Chinese.
President Donald Trump is unlikely to take the Chinese paper's advice on how to proceed. However, he left with a harsh reminder that the North Korean leader expects something in return.
However, he emphasized that the North still has trust in the US President, apparently hinting that Pyongyang wanted to keep the ongoing denuclearization talks on track.