While the US has yet to confirm the contents of the reports, they suggest that the two leaders reached more verbal agreements than they put on paper, and made public.
Pyongyang in return "commits to work toward complete denuclearisation of the Korean peninsula".
Washington is eager to see if the North's pledges were "sincere", Pompeo said, adding: "The US has been fooled before".
North Korea also serves as a valuable buffer state between China and USA forces in South Korea.
Even as Pompeo staunchly defended the summit results, he was less exuberant than Trump, who tweeted on his return to the US on Monday morning: "Just landed - a long trip, but everybody can now feel much safer than the day I took office. No longer - sleep well tonight!" And how can anyone be sure that North Korea is really denuclearizing?
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The deceased have been identified as Assistant Commandant Jitender Singh, SI Rajneesh, ASI Ramniwas and Constable Hansraj. Three others were also injured in the Pakistan firing in Jammu's Ramgarh Sector last night.
Meeting for about five hours, Trump and Kim exchanged an historic handshake, took a short stroll together, patted each other's backs and signed a summit agreement. I want to bring our soldiers back home", he said, "but that's not part of the equation right now.
Pompeo said Wednesday that Trump "made it very clear that the condition precedent for the exercises not to proceed was productive, good-faith negotiations being ongoing".
Foreign ministry spokesman Geng Shuang called on the UN Security Council to "make efforts to support the current diplomatic dialogue, efforts to denuclearise the peninsula, and promoting the process of a political settlement of the Korean peninsula issue".
In an unprecedented week for worldwide geopolitics - during which Donald Trump praised the North Korean leader shortly after disparaging Canada's prime minister - one group of people has been particularly shocked by the U.S. president's upending of diplomatic norms.
"Although not part of the joint declaration, Mr Trump said after the summit that sanctions "will come off" once the U.S. is sure that the nukes are no longer a factor". "I think it's inappropriate to be having war games".
"If diplomacy doesn't move in the right direction, sanctions will increase", Secretary of State Mike Pompeo says.
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The earlier record of 229 not out in the name former Australian captain Belinda was set when Amelia was not even born. White Ferns teenager Amelia Kerr has smashed her way into cricketing folklore with a world record knock.
"The fact is, Trump has the unique skills necessary to connect with Kim", Jordan Klepper explained at The Opposition. "My meeting with Chairman Kim was honest, direct and productive".
After a day filled with smiles and handshakes watched around the world, the United States "committed to provide security guarantees" to North Korea. "I knew it. I was the only one".
"Otto did not die in vain".
"The sanctions will come off when we are sure that the nukes are no longer a factor", Trump said at the briefing, adding, "I hope it's going to be soon".
"Kim Jong Un got what he wanted at the Singapore Summit: the worldwide prestige and respect of a one-on-one meeting with the American president, the legitimacy of North Korean flags hanging next to American flags in the background", said Paul Haenle, director of the Carnegie-Tsinghua Center.
Sen. Chris Murphy, a Democrat from CT, said in a statement the ramifications of meeting with Kim Jong Un will have "serious negative consequences for American national security", and it exposed Trump as an "unprepared, weak negotiator".
Ariana Grande se serait fiancée à son chéri
Le comédien américain Pete Davidson s'est mis à genoux pour sa petite amie, la chanteuse Ariana Grande . Il semblerait que qu'Ariana Grande ait déjà oublié le rappeur Mac Miller .
Donald Trump and Kim Jong Un became on June 12 the first sitting U.S. and North Korean leaders to meet, shake hands and negotiate to end a decades-old nuclear stand-off.