Mr Trump insisted Friday his relationship with Kim "remains good" even as his aides attempted to paper over the collapse of the high-stakes second summit which concluded last week without even a modest deal on reducing Pyongyang's nuclear programme in exchange for sanctions relief.
Carter, who served as the 39th USA president, visited North Korea in 1994 to meet Kim Il Sung toward facilitating negotiations with the Clinton administration at a time when tensions were high between Pyongyang and Washington.
"The public at home and overseas that had hoped for success and good results from the second DPRK-U.S. summit in Hanoi are feeling regretful, blaming the U.S. for the summit that ended without an agreement", KCNA reported, citing a commentary in the Rodong Sinmun newspaper.
When asked about the prospects of restarting operations at an inter-Korean factory park in the North Korean border town of Kaesong and South Korean tours to the North's Diamond Mountain resort, Kim told reporters on Friday that Seoul should "work on it".
The Sohae launch facility at the Tongchang-ri site has been used for satellite launches and engine testing but never for ballistic missile launches.
Many experts think the lack of comprehensive joint exercises will eventually likely weaken the allies' military readiness if diplomacy fails and tensions with North Korea return.More news: Tesla's V3 Supercharger cuts down charging times by half
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The official also threw cold water on a more incremental process, despite earlier allusions to the USA being open to such an approach.
The North Koreans put a smaller - relatively smaller deal on the table that experts we talk to say was meant to be a starting point.
The U.S. will pressure North Korea to give access to the site in an effort to assess whether the site is operational.
The U.S. government will seek North Korea to allow American inspectors to access a missile-launch site the regime began to restore despite its pledges, according to reports.
US Secretary of State Mike Pompeo said on Monday he was hopeful he would send a delegation to North Korea for more talks in the next couple of weeks, but that he had received "no commitment yet". The official said the Trump administration did not necessarily agree with nongovernmental analysts who believe the activity is a sign of North Korean anger following the summit.
"President Trump never codified in writing North Korea's missile and nuclear testing freeze", Markey said.
"He said there is no evidence that North Korea's work at the site signals Kim is preparing to test another intercontinental missile".
With no deal between the two nations looking likely, the United States delegation left early - later insisting further talks could be thrashed out.