According to the Associated Press, Pompeo also said he had "good" and "substantive" conversations with Kim earlier this week when Pompeo was in North Korea to bring home three American detainees.
The Panmunjom Declaration for Peace, Prosperity and Unification was signed by South and North Korean leaders, which laid out a peaceful path forward.
In the joint communiqué released after Kim's meeting with Moon last month, the South pledged to help the North modernize its railroads and highways.
Washington's focus is on disarming Kim's regime, which has recently tested what appear to be missiles capable of carrying his nuclear threat to U.S. cities.
"There's a danger here of the peace track moving more quickly than the denuclearization track", warned Abraham Denmark, an Asia expert and former senior USA defense official.
As leaders from the Group of Seven industrialised nations are expected to gather in Canada on June 8 and 9, Abe hopes to hold talks with Trump on the fringes of the summit and coordinate efforts toward resolving issues related to Pyongyang, the sources said.
Beijing has already positioned itself as a critical player that can shape the outcome of the talks, which Trump said will take place June 12 in Singapore. Trump then emerged from the plane, followed by the three men.
The recent diplomatic developments have given both China and South Korea "every reason to oppose and disregard new sanctions if the USA tries to impose them", said Bilahari Kausikan, the former head of the Foreign Affairs Ministry in Singapore. To the US, that means the North giving up the nuclear weapons it has already built.
"Frankly we didn't think this was going to happen ... it's a very important thing to all of us to be able to get these three great people out", he said.
"We're not under any illusions about who these people are. We know who we are dealing with here", said Victoria Coates, of the National Security Council.
"If North Korea takes bold action to quickly denuclearise, the United States is prepared to work with North Korea to achieve prosperity on par with our South Korean friends", said Mike Pompeo.
The Trump administration insists it will maintain its campaign of "maximum pressure" on the North until Kim has shown "substantial dismantlement" of his nuclear arsenal.
During his surprise visit to North Korea this week, Pyongyang released three U.S. detainees.
Former presidents Bill Clinton and Jimmy Carter visited after leaving office.
She added that the process involving the United States and North Korea has moved in the right direction.
And, more than two decades and multiple provocative weapons tests after the last accord, the threat from Pyongyang has only grown. For about 70 years since the Korean War, the USA and North Korea have been hostile to one another.