The White House did not immediately respond to the latest North-South talks, but White House spokeswoman Sarah Sanders said an advance team of White House and U.S. State Department officials would leave for Singapore on schedule to prepare for a possible summit there.
He also accused the Times of making up a source to cast doubt on the viability of a June 12 meeting, even though a senior administration official had expressed those sentiments in a room full of reporters.
Trump called off the meeting on Thursday, citing the "tremendous anger and open hostility", in recent statements from Pyongyang, and North Korea hardened its rhetoric toward the US, warning it was ready for a "nuclear-to-nuclear" showdown if the USA didn't follow through on the summit.
"Chairman Kim said Friday afternoon he wanted to meet without any formalities, and I accepted", Moon said Sunday in Seoul.
The pair made history when they discussed aspirations for a nuclear-free Korean Peninsula and permanent peace.
The Singapore summit had been much-anticipated since March, when Trump announced that he planned to meet with Kim following a 2017 that saw the two leaders trading personal insults and nuclear threats with one another. Kim ordered the complex to be finished by April 15 next year to mark the birthday of his late grandfather and North Korea founder Kim Il Sung.
"It was a very nice statement they put out", Trump said as he left the White House to deliver a commencement address at the U.S. Naval Academy.
Kim met Saturday with South Korean President Moon Jae-in, a key figure in brokering the U.S.
Further, on Thursday, Trump wrote a letter to Kim in which he stated that due to North Korea's hostile behavior he may delay or cancel the summit.
Japanese Prime Minister Shinzo Abe said he respected and supported the USA president's move to cancel the summit while China, Pyongyang's sole major ally, urged the two foes to "show goodwill".
Trump took action after North Korea's vice foreign minister Choe Son Hui called US Vice President Mike Pence "stupid and ignorant" for warning the dictatorship could end-up like war-torn Libya.
"The only person who can pick the ball from the net is Moon Jae-in, because he can connect the two sides and he doesn't have to keep his pride over it", he said.
The talks between Mr Trump and Mr Kim, if they were to go ahead, would be focused on ways of denuclearising the Korean peninsula and reducing tensions.
His letter followed comments from a senior North Korean official, Choe Son Hui, in which she described USA vice president Mike Pence as a "political dummy" and appeared to threaten the U.S. with nuclear war.
Moon was accompanied by South Korea's national intelligence service chief, Suh Hoon. They very much want to do it.
Trump had blamed the Pyongyang regime's "tremendous anger and open hostility" as he pulled out of the talks, saying the world had "lost a great opportunity for lasting peace". Libyan leader Muammar Gadafy was deposed and murdered by Nato-backed militants after halting his nascent nuclear programme. Kim Jong Un's comments published by the newspaper did not include any mention of his potential meeting with Trump.