A US delegation met over the weekend with North Korean counterparts at the border between North and South Korea to discuss the next steps to implementing the June 12 summit's declaration, according to the US State Department.
White House press secretary Sarah Huckabee Sanders told reporters today that she would not "confirm or any deny any intelligence reports", but "what I can tell you is that we're continuing to make progress".
Immediately following the summit, Trump also announced the US was canceling a major joint military exercise with South Korea scheduled for August, Ulchi Freedom Guardian - even calling it a "war game", and "provocative" - the same language used by North Korea and China.
The Washington Post reported Saturday that US intelligence officials had evidence showing that North Korea does not intend to give up its entire nuclear stockpile, despite Trump's claim that there is "no longer a nuclear threat" from the country after the Singapore summit.
Bolton said the United States was going into nuclear negotiations aware of Pyongyang's failure to live up to its promises in the past.
Evidence collected since the summit points to preparations to deceive the USA about the number of nuclear warheads in North Korea's arsenal as well as the existence of undisclosed facilities used to make fissile material for nuclear bombs, according to the report. Kim may want to give up his weapons but the generals may not. He said that would include transparency by North Koreans about the nuclear material they have, the engineering of it and the missiles that would deliver those nuclear weapons as well as other weapons of mass destruction.
The North's Korean Central News Agency reported on Monday. that Kim made on-site inspections of two textile plants in the northwestern town. a day after he went to a cosmetics factory in the same area.
"To prove North Korea's willingness to denuclearize, at the minimum, there should be an agreement on the basic roadmap on denuclearization of North Korea - the definition, timeframe and verification procedures and the ways to guarantee the North Korean regime", said Park Won-gon, a professor at Handong Global University.
"Kim Jong-un was very emphatic in Singapore".
The national security adviser added that "there's nobody involved in this discussion with North Korea in the administration who is overburdened by naïveté. If not for me, we would now be at War with North Korea!"
A bad outcome for South Korea and Japan would be Trump agreeing to a deal that removes North Korea's long-range missiles that pose a direct threat to continental United States, but leaves Kim's shorter arsenal mostly intact.
This also comes ahead of U.S. Secretary of State Mike Pompeo's scheduled visit to Pyongyang later this week.
The lone weapons facility that has been acknowledged by North Korea is in Yongbyon, 60 miles north of Pyongyang.
While North Korea made a public show in June of demolishing the country's main nuclear weapons test site, there has been little public evidence of efforts to dismantle scores of other sites linked to production of nuclear and chemical weapons and delivery systems.
The US and North Korea have expressed different expectations for the pace and sequence of North Korea's disarmament and relief from worldwide sanctions.