Kim had flown in from Beijing and Pompeo from Washington.
Trump says his meeting with the most senior North Korean to visit the White House in 18 years lasted longer than expected. Kim is the highest-ranking North Korean official to visit the USA in 18 years.
Mr. Pompeo began his discussions with Gen. Kim by hosting a dinner on Wednesday night.
"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 Lavrov.
Pompeo also appeared to lower expectations of what might come out of a summit, after a NY meeting with Kim. "Steak, corn, and cheese on the menu".
"We welcome contacts between North and South Korea, as well as between North Korea and the United States", Lavrov said on May 31 after meeting with North Korean Foreign Minister Ri Yong Ho, according to Russia's TASS news agency.
Trump and Kim spent more than an hour in the Oval Office on Friday discussing issues in the run-up to a June 12 summit in Singapore between Trump and Kim Jong Un.
A man watches a television news screen showing US President Donald Trump, left, and North Korean leader Kim Jong Un, at a railway station in Seoul on May 25, 2018.
"I look forward to the day when I can take the sanctions off of North Korea", Trump said.
The president said he believed Kim wanted a deal. The two sides do not expect to sign any agreement on June 12, he said.
If the North Korean delegation goes to the White House, it would be the first visit there by high-level officials from there since 2000 when Jo Myong Rok, a marshal, met President Bill Clinton.
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North Korea, whose nuclear ambitions have been a source of tension for decades, has made advances in missile technology in recent years and its nuclear arsenal now threatens the United States.
The contents of Kim's letter to Trump have been the source of speculation since Trump announced the letter's existence Thursday.
Trump-Kim summit: North Korea's ex-spy chief meets Pompeo in NY.
Trump said he and Kim Yong Chol "talked about a lot of things" in the Oval Office.
The North Korean official is carrying a letter to Trump from Kim Jong Un.
Trump then called the bluff by canceling the summit himself in a letter to Kim, to which North Korea responded with conciliatory statements, saying it would meet the United States any time. A letter being delivered to me from Kim Jong Un.
Since Trump's abrupt cancellation last week of the historic meeting with Kim, there's been an global scramble to salvage the event - with rapid-fire diplomacy efforts in the USA, on the Korean Peninsula and in Singapore, the Southeast Asian city-state hosting the summit.
It was not immediately clear who accompanied Kim Yong Chol on the North Korean side.
The visit marks the second time in history a North Korean official has visited the White House.
However, Trump on Thursday conceded for the first time that the negotiations with Pyongyang might require more than one summit.
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