The vice president's comments also echoed those of Trump's national security advisor, John Bolton, who had suggested the U.S. could pursue a Libya-style denuclearization plan with North Korea. Years after that nuclear deal, Libyan leader Moammar Gadhafi was overthrown and slain, a move the U.S. supported. North Korea's Kim is concerned about regime change.
Trump's cancellation earned quick praise from Republican lawmakers. Sen. Marco Rubio, R-Fla., said in a tweet that the president's move was "100% the right decision."
House Speaker Paul Ryan also weighed in, but in more measured tones.
"The North Korean regime has long given ample reason to question its commitment to stability," Ryan said in a statement. "We must continue to work with our allies toward a peaceful resolution, but that will require a much greater degree of seriousness from the Kim regime."
Trump's critics also seized on the news, but as a way to hammer the White House.
"The art of diplomacy is a lot harder than the art of the deal. The reality is, is that it's pretty amazing that the administration might be shocked that North Korea is acting as North Korea might very well normally act," Sen. Bob Menendez, D-N.J., said in a hearing involving Secretary of State Mike Pompeo.
While he was still CIA director, Pompeo met with Kim over Easter weekend to establish diplomatic ties and work toward setting up the summit. Pompeo had also secured the release of the three American prisoners released by North Korea earlier this month.
In his letter to Kim, Trump thanked him for the release but referred to the prisoners in non-diplomatic language.
"I want to thank you for the release of the hostages who are now home with their families. That was a beautiful gesture and was very much appreciated," Trump said.
At the Senate Foreign Relations, Pompeo said Thursday that North Korea did not respond to preparation teams for the summit.
There were no immediate details about how the administration would continue to pursue diplomacy with North Korea, which is the only nation to conduct nuclear-weapons tests this century. Yet Trump left the door open for arranging a new meeting with Kim.
"If you change your mind having to do with this most important summit, please do not hesitate to call me or write," the president wrote. "This missed opportunity is a truly sad moment in history."
Read the full text of the letter here:
May 24, 2018
Kim Jong Un
Chairman of the State Affairs Commission of the Democractic People's Republic of Korea
Dear Mr. Chairman:
We greatly appreciate your time, patience, and effort with respect to our recent negotiations and discussions relative to a summit long sought by both parties, which was scheduled to take place on June 12 in Singapore. We were informed that the meeting was requested by North Korea, but that to us is totally irrelevant. I was very much looking forward to being there with you. Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate, at this time, to have this long-planned meeting. Therefore, please let this letter serve to represent that the Singapore summit, for the good of both parties, but to the detriment of the world, will not take place. You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used.
I felt a wonderful dialogue was building up between you and me, and ultimately it is only that dialogue that matters. Some day, I look very much forward to meeting you. In the meantime, I want to thank you for the release of the hostages who are now home with their families. That was a beautiful gesture and was very much appreciated.
If you change your mind having to do with this most important summit, please do not hesitate to call me or write. The world, and North Korea in particular, has lost a great opportunity for lasting peace and great prosperity and wealth. This missed opportunity is a truly sad moment in history.
Donald J. Trump
President of the United States of America
CNBC's Eamon Javers and Amanda Macias contributed to this report.