The president has indicated that he is open to inviting the North Korean leader to a follow-up summit at his Mar-a-Lago resort in Palm Beach, Florida.
"I think it's a 'getting to know you" meeting, and that could be a very positive thing", he noted about the upcoming summit.
"The US government's trade measures, citing its security, makes us concerned that they could disrupt the global market", government spokesman Yoshihide Suga told reporters on Monday.
Perez declined to confirm Rodman's plans to travel to Singapore, saying plans were in the process of being finalized and that an official announcement will be made in the coming days.
Hours earlier a senior North Korean official had questioned the value of the talks and said her country was just as ready to meet in a nuclear confrontation as at the negotiating table.
But North Korea responded harshly.
Trump is scheduled to meet with Kim on June 12 in Singapore to discuss nuclear disarmament on the Korean Peninsula.
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While the North has kept mum on its summit preparations, Trump's and his Twitter messages are a rare "credible" source of relevant information.
Bolton has not commented publicly since the president distanced himself from the Libya comparison and the White House insisted he would follow the "Trump model".
After an escalation of rhetoric between United States and North Korean top diplomats, Mr Trump last month briefly called off the talks.
Trump said he had talked with the North's envoy on the matter.
"You've got to lose some weight too", says the banner for the gym, which shows a photograph of the portly North Korean leader next to a bikini-clad woman.
"I think that denuclearizing one state is enough for me", the prime minister replied, apparently referring to his staunch opposition to the 2015 Iran nuclear deal. "It's not going to happen all in one meeting".
"The Ambassador and Secretary Pompeo have been working hand-in-hand providing the president national security options and foreign policy advice, frankly whether it involves the summit, Syria or other issues", Special advisor to President Trump and National Security Counsel spokesperson Garrett Marquis said Thursday.