In a letter to Un, Trump said the meeting was canceled based on "tremendous anger and open hostility" displayed in a recent statement.
In a statement, the North Korean government referred to Vice President Mike Pence was a "political dummy" and said it is just as ready to meet in a nuclear confrontation as at the negotiating table.
The letter stated that Trump felt it was "inappropriate, at this time, to have this long-planned meeting."
"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," the letter continued.
The president called the cancellation a missed opportunity for peace.
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."
Trump ended the note stating that he hopes to have a meeting in the future and thanked him for releasing the American hostages.
The cancelation came just hours after reports that North Korea demolished a nuclear test site in the northeast mountains.
The Associated Press contributed to this post