The United States has offered to pay, but some are afraid the North Koreans will take offense to that.
After the meeting, the North Korean delegates chatted with Trump on the White House lawn.
Eight minutes later, according to the Washington Post, Trump admitted that he hadn't even opened the letter when a reporter asked if he sent anything back.
The U.S. insists that North Korea must give up all its nuclear weapons before it can shed its pariah status or get any relief from a crushing sanctions regime.
The president teased reporters about the contents of the letter, saying, "That letter was a very nice letter".
The summit is set to be held on June 12 in Singapore.
"Good working dinner with Kim Yong Chol in NY tonight", Pompeo tweeted.
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Trump cancelled the on-off North Korea summit in late May, blaming the country's "tremendous anger and open hostility".
"I am going to visit the DPRK and meet..." "We can go fast; we can go slowly".
Citing two people familiar with the talks, the Post reported earlier that the U.S. is open to covering the costs, but is considering asking the host country, Singapore, to foot the bill. "The relationships are building and that's a very positive".
Previous attempts at nuclear diplomacy with the North by Presidents Bill Clinton and George W. Bush fell apart.
South Korean Unification Minister Cho Myoung-gyon (l) shakes hands with Ri Son-gwon from North Korea's Committee for the Peaceful Reunification of the country.
Kim said even after learning these details, it's hard to expect what the results of the summit could be.