Pompeo, however, said that it was still unclear whether the meeting would take place on June 12 or at a later date.
"We're going to start a process", he said.
Shortly after 1 p.m., a black sport utility vehicle entered the White House grounds and pulled up to the South Portico, where Kim Yong Chol, a former spy chief who is leading the North Korea side in pre-summit talks, stepped out.
Trump told reporters he hadn't yet read the letter from Kim and added with a smile, "I may be in for a big surprise, folks".
The president said he expected a number of summits would be needed to settle all outstanding issues.
Mr Trump last week called off the summit after North Korea expressed anger at comments by USA officials.
"I am confident we are moving in the right direction", Pompeo told reporters at a news conference in NY after meeting Thursday with former North Korean military intelligence chief Kim Yong Chol. "I haven't opened it", he said.
"I think you'll have a very positive result in the end - not from one meeting", Mr. Trump said.
Analysts say that depends on whether still- formidable hurdles can be overcome.
Kim Yong Chol, vice chairman of the North Korean ruling party's central committee, was allowed into the United States despite being on a US sanctions list.
Pyongyang insists it wants to denuclearize the entire Korean peninsula, which would mean ending the US military presence there, a demand few believe the USA would ever accept.
While Trump would score points internationally and domestically by pulling off the summit and softening his hardline image by having the summit, Kim appears to be equally invested in the denuclearisation talks that could translate to economic development for his impoverished country that is under severe economic sanctions.
While nuclear weapons are believed to be play an important part in the survival of North Korea.
Pompeo's meetings in New York City included Kim Yong Chul, the top aide who will carry Kim Jong Un's letter to Washington. Chol is also one of the closest allies to the supreme leader of North Korea, Kim Jong Un.
"I look forward to the day I can take the sanctions off North Korea", Trump said.
"We are meeting with the Chairman (Kim Jong-un) on June 12 (in Singapore)".
Earlier this month, President Donald Trump suddenly announced a cancellation of the summit, before reversing course 24 hours later. President Trump has offered to help rebuild the North's economy if it scraps its nuclear weapons. "We welcome the summits that already took place between Pyongyang and Seoul as well as planned meetings between North Korean and USA leadership".
- LeBron James’ injured hand calls to mind some what
- Net Neutrality Repeal Takes Effect Monday
- Nadal completes fightback to reach 11th French Open semi final
- Singapore hotel offers 250 free Trump-Kim burgers to celebrate summit
- New Delhi wants North Korea-Pakistan nuclear axis addressed
- White House: North Korea talks moving 'more quickly than expected'
- Fallout 76 PS4 Xbox One Release Date, Preorders with BETA LIVE!
- 'Fallout 76' to take place in West Virginia
- Final preparations under way for Trump-Kim summit
- Putin calls for boosting trade ties among SCO members