This is seen as part of South Korea's efforts to mediate the negotiations between North Korea and the USA,. after their leaders failed to come to an agreement in their 2nd summit last week.
Bolton also said the potential for denuclearization remains with President Trump, previously extending he would like to keep the relationship between the US and North Korea.
"The President takes him (Kim) at his word", Mr Bolton told Tapper.
Rogers then blamed Trump for setting up Kim Jong-un as an worldwide player, which he viewed as very risky.
But Bolton maintained Sunday that Trump is "not desperate for a deal - not with North Korea, not with anybody - if it's contrary to American national interests".
Moon helped set up the first meeting between Trump and Kim last June when they agreed to a vague aspirational statement about a nuclear-free Korean Peninsula without describing how and when it would occur. Trump and Kim's second summit last week collapsed over what the Americans saw as excessive North Korean demands for sanctions relief in exchange for limited disarmament steps.
Trump and Secretary of State Michael Pompeo said they couldn't accept the proposal from North Korea to shut down the Yongbyon complex in return for complete sanctions relief because the regime still had hidden production facilities and missiles elsewhere that could threaten the US.
"For the Democrats to interview in open hearings a convicted liar & fraudster, at the same time as the very important Nuclear Summit with North Korea, is perhaps a new low in American politics and may have contributed to the "walk", Trump said on Twitter.
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Also read | Failed Hanoi meeting has U.S. allies in region asking: What's next? "While I believe the United States-North Korea negotiations will eventually reach an agreement, it's never desirable for a vacuum in dialogue or stalemate to prolong", he said, urging South Korean officials to find ways so that Washington and Pyongyang can narrow their differences.
"This is, I think, the result of a president who is not prepared for these kinds of negotiations, a staff that is not well-prepared and is essentially flying by the seat of its trousers".
The president said he believed Kim's claim that he didn't know what happened to Otto Warmbier, who died at age 22 days after being sent back to the United States in 2017.
The spokesman said on Sunday that South Korea would pursue "behind-the-scenes" meetings with the North, possibly including sending a special envoy to Pyongyang.
"The reason I do not want military drills with South Korea is to save hundreds of millions of dollars for the USA for which we are not reimbursed", Trump tweeted Sunday.
"That was my position long before I became president", Trump tweeted Sunday while adding "reducing tensions with North Korea at this time is a good thing".
Opponents of scrapping the drills warn that it could affect the combat readiness of US and South Korean forces and hand the North a strategic advantage on the divided peninsula.