Trump blamed "open hostility" from North Korea for his decision to call off the planned talks with Kim Jong-un, and warned Pyongyang against committing any "foolish or reckless acts".
In a personal letter to Kim, Trump announced Thursday he would not go ahead with the June 12 summit in Singapore, following what the White House called a "trail of broken promises" by the North, AFP reported.
China, Pyongyang's sole major ally, urged the two foes to "show goodwill" as regional powers braced for the possible diplomatic fallout.
"Stay patient, show goodwill, move in the same direction and continue to stay committed to promoting the denuclearization of the peninsula," Foreign Ministry spokesman Lu Kang told a regular press conference.
So far Pyongyang's reaction to the sudden U-turn has been conciliatory.
First Vice Foreign Minister Kim Kye Gwan called Trump's decision "unexpected" and "regrettable". But he left the door open for talks, saying officials were willing "to sit face-to-face at any time".
Just before Trump announced the cancellation of the meeting, North Korea declared it had "completely" dismantled its nuclear test site in the country's far northeast, in a carefully choreographed goodwill gesture ahead of the summit.
But the chances of success for the unprecedented face-to-face had recently been thrown into doubt as threats were traded by both sides.
Trump's announcement came a day after Pyongyang hardened its rhetoric, calling comments by Vice President Mike Pence "ignorant and stupid".
"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," read Trump's letter to Kim.
But he said talks could still go ahead "at a later date".
The decision blindsided treaty ally South Korea, which until now had brokered a remarkable detente between Washington and Pyongyang.
South Korean President Moon Jae-in called the move "shocking and very regrettable" but his government vowed to push ahead with improving ties with the North.
UN Secretary-General Antonio Guterres urged the parties to keep talking, as did host Singapore, while Russia's President Vladimir Putin held out hope that dialogue would resume and the talks would eventually take place.
Trump, however, said on Friday he was pleased that North Korea said it was still open to talks after his abrupt cancellation of a planned June 12 meeting.
"Very good news to receive the warm and productive statement from North Korea. We will soon see where it will lead, hopefully to long and enduring prosperity and peace. Only time (and talent) will tell!" Trump said on Twitter.