He said in the letter that the world is losing a "great opportunity for lasting peace and great prosperity and wealth" now that the summit has been cancelled.
"The North Koreans didn't tell us anything". "If you change your mind having to do with this most important summit, please do not hesitate to call me or write".
And in a statement later at the White House, Mr Trump said he was still open to dialogue but had spoken to Defence Secretary Jim Mattis and warned North Korea against any "reckless act".
Mr Trump's letter came shortly after North Korea followed through on a pledge to blow up tunnels at its nuclear site in the presence of foreign journalists.
He said the U.S. military was the most powerful in the world and was ready if necessary.
South Korean President Moon Jae-in, who worked hard to help set up the summit and urged Trump at a White House meeting on Tuesday not to let a rare opportunity slip away, said he was "perplexed" by the cancellation.
The White House viewed North Korea's objection to a routine US-South Korean joint military exercise - and its recent cancellation of a meeting with the South Koreans - as a breach of its commitments leading up to the summit.
"The United States will also have to undertake careful deliberations about the fate of the planned North Korea-U.S. summit in light of this provocative military ruckus jointly conducted with the South Korean authorities", North Korea's Korean Central News Agency said.
The outlook for the meeting soured dramatically this month when North Korea angrily rejected the notion that it would agree to unilateral nuclear disarmament as Washington has demanded.
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"I hope that Kim Jong-un will ultimately do what is right, not only for himself, but perhaps most importantly what's right for his people, who are suffering greatly and needlessly."
Pompeo said the USA had tried in recent days to put teams together to prepare for the meeting and "we had received no response to our inquiries from" the North Korean government.
Mr Pompeo read the letter aloud at the start of testimony to the committee, saying it was a disappointing development although "frankly not a surprise".
"I think, by and large, the president's message was polite, although his reference to the US nuclear arsenal looked a little threatening to me", said Christopher Hill, the lead USA negotiator with North Korea under the George W. Bush administration.
"Over the past many days we have endeavoured to do what Chairman Kim and I had agreed, to put preparation teams together to begin to work for the summit, and we had received no response to our inquiries to them", Mr Pompeo said. Moon has invested a lot of political capital in improving relations with North Korea, although Pyongyang just broke off a high-level meeting with Seoul over U.S.
Foreign leaders reacted with dismay to the summit collapse, with South Korean President Moon Jae-in expressing "deep regret" and summoning top security aides for emergency talks.
Trump has said he detected a change in Kim's attitude after the second of two recent visits the North Korean made to China and that he was possibly being influenced by Beijing, with which the United States is embroiled in a major trade dispute.
UN Secretary-General Antonio Guterres said he was "deeply concerned".
He said leaders had a responsibility to minimise the risk of weapons and said disarmament was a concern for every country and should cover weapons "from hand grenades to H-bombs".