Trump said it was “inappropriate” to have a summit at this time amid heightened tensions with North Korea.
The US President said it was a “missed opportunity” and a “truly sad moment in history”.
And he warned North Korea of his “massive and powerful” nuclear arsenal.
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“I was very much looking forward to being there with you,” Trump said in the letter.
“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.”
North Korea had previously furiously attacked the US, calling vice-president Mike Pence stupid and raging over the deployment of B-52 nuclear bombers near the Korean Peninsula.