The content of the letter was not immediately known, but according to the Wall Street Journal, Kim Jong-un is believed to have expressed interest in a summit meeting with Trump. "We understand there's a letter coming, and we look forward to receiving that letter and are trying to work towards our ultimate goal of denuclearisation", he said.
After the meeting, which lasted more than an hour, Trump walked Kim out of the White House and they continued to speak and posed for a photo before Kim got into a black SUV and departed.
"I haven't seen the letter yet". Trump cancelled the June 12 summit last week, then suggested it could still happen.
If the meeting went ahead it would be the first between Mr Kim and another head of state in Pyongyang.
"A letter is going to be delivered to me from Kim Jong Un", Trump said.
Analysts say that depends on whether still- formidable hurdles can be overcome.
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.
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.
Trump says historic summit with Kim Jong-un is back on for June 12
Despite having a border with North Korea and relatively cordial relations that Putin has seemed to want to develop further, Russian Federation has kept a surprisingly low profile as Kim has emerged onto the world stage this year, meeting twice with Chinese President Xi Jinping and South Korea's Moon.
Pompeo said they finished everything they needed to address in the morning session.
North Korea has developed nuclear devices as well as missiles capable of reaching the USA mainland heightening the risks for Washington.
Meanwhile North Korean leader Kim Jong Un has reportedly said that he hopes a phased approach will be used to resolve the issues of relations with the United States and the denuclearization of the Korean Peninsula.
In recent months he met both Chinese president Xi Jinping and South Korean president Moon Jae-in in a flurry of diplomacy culminating in a summit with Donald Trump in Singapore on 12 June.
The announcement reversed an earlier decision from Trump to cancel the meeting on the North's nuclear program.
"I never said it goes in one meeting", Mr. Trump said.
Trump told reporters that denuclearization - and a formal end to the decades-old Korean war - would be on the table in Singapore.
North Korea's flurry of diplomatic activity following a torrid run in nuclear weapons and missile tests in 2017 suggests that Kim is eager for sanctions relief to build his economy and the global legitimacy the summit with Trump would provide.
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