Trump's fortunes seemed to shift Friday, as the North Korean government said it is still "willing to give the US time and opportunities" to reconsider talks "at any time, at any format".
"We reiterate to the United States that we are willing to sit face to face at any time and in any way", said Kim, who has negotiated with United States counterparts for years.
Earlier Friday, in a tweet, he had called the North's reaction to his letter canceling the summit "warm and productive".
Democratic members say it is Trump and his House GOP allies who are attempting to delegitimize the investigation and erode the credibility of witnesses like former FBI Director James B. Comey.
Minutes before his Friday morning tweet, Trump claimed Democrats were "rooting" against his administration in its negotiations with North Korea.
"Nothing we heard today has changed our view that there is no evidence to support any allegation that the Federal Bureau of Investigation or any intel agency placed a spy in the Trump campaign", Schiff said as he read a statement he said represented his views and those of his party's House and Senate leadership.
"I would like to conclude that President Trump's statement on the North Korea-US summit is a decision that is not in line with the wishes of the who hope for the peace and stability of the Korean peninsula as well as the world". "We're not going to give them that capability".
BPR reported Thursday that North Korea demolished its Punggye-ri nuclear test site, fulfilling a commitment made by the Kim regime last month, just before Trump cancelled the summit. They very much want to do it.
The president, in his letter, said he felt the sit down would be "inappropriate at this time" given Kim's recent "anger and open hostility".
White House spokeswoman Sarah Sanders told reporters Trump did not want a meeting that was "just a political stunt".
At a late afternoon briefing Thursday, a senior administration official described the recent interactions between the USA and North Korea as "a trail of broken promises".
North Korean Vice Foreign Minister Kim Kye-gwan, in response to Trump's comments, said "there is a willingness to sit down at any time, in any way, to solve the problem", North Korea's state-run Korean Central News Agency reported. "Only time (and talent) will tell!" the United States president said in a tweet.More news: Harvey Weinstein surrenders to police in sex assault probe
It was unclear whether Trump was engaged in what he saw as a negotiating ploy or if his moves were a manifestation of mounting internal concerns over ensuring a successful outcome for the summit.
The North Koreans were a no-show for a preparatory meeting in Singapore last week, part of a trail of broken promises, lack of good faith and poor communication prompting the president's decision, according to administration officials. And I said you've got two choices - containment, which is give them a nuke and a missile and tell them if they ever use it, we'll blow you off the map.
The South Carolina Republican also told Fox News that the next step for Trump is to reprimand China for seemingly undercutting USA diplomatic efforts with North Korea after a meeting Kim had in early May with Chinese President Xi Jinping.
While the Trump administration had insisted on North Korea's complete, verifiable and irreversible dismantling of its nuclear program, Pyongyang had always couched its language in terms of denuclearization of the Korean peninsula. He told reporters Friday that "everybody plays games". The president did not call South Korean President Moon Jae-in or Japanese Prime Minister Shinzo Abe to inform them of it, White House officials confirmed.
"This is North Korea 101", says Suzanne DiMaggio, a senior fellow at the New America Foundation.
President Donald Trump responded to the statement on Twitter.
North Korea had threatened to pull out of the unprecedented summit after US officials called for the so-called Libya model approach, which involved that African country's total nuclear dismantlement before any concessions were granted.
In recent months, Trump had traded his bellicose threats of "fire and fury" for bouquets of flattery, calling Kim "very honorable" and exuding confidence that he could seal a deal that had eluded his predecessors for generations. The next morning, he consulted with Secretary of State Mike Pompeo and national security adviser John Bolton before deciding to scrap the summit.
A number of analysts tell VOA News there could still be a Trump-Kim summit soon.
"Don't cancel your reservations for Singapore just yet", former US deputy secretary of state Anthony Blinken told VOA's Korean Service. "This is unlikely to be the final word".
"I really believe Kim Jong Un wants to do what's right", the USA president said at one point.
Speaking to reporters at the Pentagon on Friday, Mattis said diplomats are working to get the summit back on track.