The statement cited US officials who are "going against President Trump" and his intent to advance relations between the two nations, saying that the president has expressed "gratitude to our goodwill measures" implemented as part of the agreement.
The statement was also published by KCNA.
"However, the USA responded to our expectation by inciting global sanctions and pressure".
The mission described as "reckless" a remark from Guterres who said that North Korea "can be a normal member of the worldwide community in this region through total denuclearization that is verifiable, irreversible". The letter was handed to North Korean Foreign Minister Ri Yong Ho during the weekend.
US National Security Advisor John Bolton has also weighed in on the issue, saying Sunday that nobody in Trump's administration is "starry-eyed" about the prospect "of North Korea actually denuclearising".
North Korea has made clear it felt the Singapore summit was only a first step, and that its own concessions - such as freezing nuclear and missile tests and the returning of remains - should be reciprocated by the USA in some manner.
But across the region, there have been signs that U.S. President Donald Trump's campaign for "maximum pressure" lost steam after Pyongyang sought to improve relations with Washington, Seoul and Beijing.
The "Fox & Friends" transition has garnered criticism due to the light-hearted nature of discussing the North Korean dictator, who has been under fire for human rights violations and nuclear testings.
North Korea has in the past expressed anger over comments made by administration officials in the media, especially Bolton.
"We need to reveal who might have violated United Nations sanctions resolutions or whether the government was aware of (the entry of suspected ships)", he said.
North Korea has called on the United States to reciprocate its "goodwill measures" by easing sanctions and stopping demands that the North denuclearise first, which they branded insulting.
Kim vowed in Singapore to work toward denuclearization, but the two sides have yet to define a deal to meet that goal and Washington insists sanctions pressure must be maintained during negotiations.
After the meeting, however, US intelligence leaders were concerned that it appeared North Korea was being deceptive because the nation was actually boosting nuclear weapons at multiple "secret sites".
Pyongyang has made clear it views a peace treaty and a security guarantee from the United States that Washington will not attack it as a key step in the process towards full denuclearization, and Thursday's statement appeared to express frustration at the lack of progress on these fronts.