The president penned an extraordinary open letter, released by the White House, in which he said he feels it is "inappropriate at this time, to have this long-planned meeting."
In a statement, the North Korean government had referred to US vice president Mike Pence as a "political dummy" and said it is just as ready to meet in a nuclear confrontation as at the negotiating table.
Earlier on Thursday North Korea demolished its nuclear test site ahead of the planned summit.
The meeting, which came about after North Korea said it was committed to denuclearising the Korean peninsula, was scheduled to take place on June 12.
Below is the full text of the letter President Donald Trump sent to North Korea's Kim Jong Un.
Donald Trump's letter to Kim Jong Un
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 the 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 latest peace and great prosperity and wealth. This missed opportunity is a truly sad moment in history.
Donald J Trump