"Remember what I say, we will see what we will see", he said.
"I'd like to see it done in one meeting". He added, "I think you're going to have a very positive result in the end. We talked about ending the war", Trump said.
Later, he said that he had not read it yet: "I may be in for a big surprise, folks".
The Oval Office talks and letter delivery came only a week after Trump threatened to consign the entire process to history, abruptly cancelling the summit in a sharply worded letter, only to revive preparations shortly afterwards.
The visit marks the second time in history a North Korean official has visited the White House.
With the scheduled June 12 summit approaching, Kim's letter has put the ball back in Trump's court.
Top American and North Korean officials are holding a full day of meetings in NY on Thursday aimed at deciding whether a summit between President Donald Trump and North Korean leader Kim Jong Un can be salvaged.
Trump wrote in his letter last week that the talks would be "inappropriate" following the "hostility" from North Korea.
"I look forward to the day when I can take the sanctions off of North Korea". He was met outside the West Wing by the White House chief of staff, John Kelly, and the head of the CIA Korea department, Andrew Kim, who ushered the 72-year-old regime veteran into the Oval Office to meet Trump and hand over a personal letter.
Mr Pompeo told a press conference that he was confident talks with North Korean officials were moving in the right direction towards a historic summit between the two countries.
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Who is Kim Yong-chol, the North Korean official representing Kim Jong-un?
"We had hundreds of new sanctions ready to go", he said, but that they wouldn't be imposed "until the talks break down".
Kim Yong Chol left his hotel in New York City early Friday for the trip to Washington in a convoy of SUVs.
US Secretary of State Mike Pompeo (2nd L) holds talks with North Korean envoy Kim Yong-chol (2nd R) in NY, on May 31, 2018.
Kim says he is committed to "denuclearisation" in some form, but he is expected to demand security guarantees - one of which could be an formal end to the conflict with the US and South Korea.
"We will push forward to test the proposition that we can achieve that outcome", he said.
The North Korean visit to the White House on Friday will be the first since 2000, when President Bill Clinton met senior figure Jo Myong-rok in an unsuccessful attempt to win the reclusive nation's nuclear disarmament.
He wants North Korea to give up its nuclear arms in return for sanctions relief, but the Pyongyang leadership has seen the nuclear program as crucial to its survival and says it can not give it up without security guarantees.
Disputes between Washington and Pyongyang led Trump to cancel the June 12 meeting on May 24 - only to see a flurry of diplomatic efforts surrounding the proposed summit in recent days.