Kim delivered a letter to Trump Friday from Kim Jong-Un, reportedly confirming his commitment to nuclear talks.
Gen Kim Yong-chol's visit came a day after he met US Secretary of State Mike Pompeo in NY, who described their talks of denuclearisation as "substantive".
The president, however, did not want to raise expectations. "Hopefully we will have a meeting on the (June) 12th", Trump said, adding there may be multiple meetings but "maybe we'll have none".
Trump indicated he's continuing to use a carrot-and-stick approach to diplomacy.
The president said the US government would not put in place any new sanctions while talks were taking place. "I said I'm not going to put them on until such time as the talks break down". U.S. and North Korean envoys have also been meeting in Panmunjom in the Demilitarised Zone between North and South Korea, and an American team is in Singapore to make logistical arrangements for the meeting.
"It will take bold leadership from Chairman Kim Jong Un if we were able to seize this once in a lifetime opportunity to change the course for the world", he said. "You're talking about 70 years". Much like his latter-day counterpart would 18 years later, Jo Myong Rok, first vice-chairman of North Korea's National Defence Commission, delivered to Clinton a personal letter from the country's leader, Kim Jong Il, the father of Kim Jong-un.
Shortly after leaving the meeting venue at the residence of the deputy U.S. Ambassador to the United Nations, Pompeo tweeted: "Substantive talks with the team from #NorthKorea".
Pompeo spoke to reporters in NY after meeting Thursday with Kim Yong Chol, the former military intelligence chief.
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The president teased reporters about the contents of the letter, saying, "That letter was a very nice letter".
The president had withdrawn from the summit on May 24 with a strongly worded letter of his own, citing "tremendous anger and open hostility" by Pyongyang but also urged Mr Kim to call him. "But I see over a period of time".
He later said he had not yet opened the letter.
Trump said he did not bring up the rogue regime's murderous human rights record.
"This summit will be historic by its very nature".
North and South Korea are resuming senior-level peace talks that Seoul sees as an important step in building trust with Pyongyang amid a USA -led diplomatic push to persuade the North to give up its nuclear weapons. "As we move to adjust to the political situation in the face of USA hegemonism, I am willing to exchange detailed and in-depth opinions with your leadership and hope to do so moving forward", Kim told Sergey Lavrov.
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.