A senior White House official also said planned joint coordinating sessions scheduled to take place in Singapore last week never happened because U.S. officials including the White House deputy chief of staff were "stood up". A scrapping of diplomacy could see a return to the torrent of weapons tests - and the fears of war they created - that North Korea unleashed previous year as it sought to put the finishing touches on a nuclear-armed missile program meant to target the entire US mainland.
"It was a very nice statement they put out", Trump told reporters in Washington before departing the White House to visit the US Naval Academy in Annapolis, Maryland. "We'd like to do it".
While Trump's letter to Kim clearly left the door open for a future summit, speculation about such a meeting is futile, noted the scholars, until the White House comes up with a coherent North Korea strategy that includes tangible incentives for Pyongyang.
And Mr Trump added: "Everybody plays games".
Several Western journalists were at the Punggye-ri test site in North Korea, pictured here via satellite, to witness its destruction.
Major Garrett, chief White House correspondent for CBS News. "Our commitment to doing our best for the sake of peace and stability for the world and the Korean Peninsula remains unchanged, and we are open-minded in giving time and opportunity to the USA".
Trump indicated the summit could be salvaged after welcoming a conciliatory statement from North Korea saying it remained open to talks.
Earlier on Friday South Korean president Moon Jae-in urged Mr Trump and Kim Jong-un to talk directly to each other. Given his mercurial personality, is it possible, many South Koreans wonder, that Mr Trump might resort to some sort of pre-emptive strike despite the horrendous loss of life that would nearly certainly entail.
A military parade in North Korea marks the 105th anniversary of the birth of the country's founding father, Kim Il Sung in Pyongyang on April 15, 2017.
EPANorth Korea has conducted six nuclear weapon tests in the tunnels of the underground site since 2006
The foreign ministry in Pyongyang had referred to US Vice President Mike Pence as a "dummy".
Trump told reporters on his way to board the presidential helicopter that US officials are in talks with North Korea after the country's "very nice statement." on Friday.
On Thursday, Trump sent a letter to Kim announcing his decision to cancel the summit.
President Trump proved he is not messing around when it comes to his stance on North Korea; reaction on "Hannity" to the decision to pull out of North Korea summit.
President Moon said on Thursday that it was trying to figure out Mr Trump's intentions in cancelling the summit.
We asked analysts what Trump's decision means for the U.S.
USA president Donald Trump said his administration is in contact with North Korea and that a June 12 summit with the country's leader Kim Jong-un might take place, a reversal of comments the White House made a day earlier. North Korea also indicated willingness to resume negotiations with the U.S.
"It appears that (the North) remains honest in implementing the agreement and making efforts on denuclearization and peace building", added the minister in charge of inter-Korean affairs.
In the city's Gwanghwamun Square Friday, a group of about 30 protesters holding the banners of South Korea's left-wing Minjung party had gathered to demonstrate against the cancellation of summit.
"I think [canceling the June 12 summit] shows how inconsistent Trump is with his policies", a 21-year-old student at Seoul's National University told TIME. But Democratic Senator Brian Schatz said the move was what happened "when amateurs are combined with warmongers".