Pompeo held firm to Trump's position that sanctions will remain in place until North Korea denuclearizes - and said they would even increase if diplomatic discussions did not progress positively.
Last year, about 50,000 South Korean and 17,500 USA troops participated in Ulchi-Freedom Guardian, billed as the world's largest command-and-control exercise and aimed at defending against a North Korean attack.
"Our Country's biggest enemy is the Fake News so easily promulgated by fools!"
Trump's pledge to end joint exercises with South Korea without explicit concessions from North Korea to lower the military threat posed by Pyongyang took South Korean and USA military officials by surprise.
On the issue the world has been most fixated on - North Korea's pursuit of a nuclear arsenal meant to target the entire United States mainland - Trump and Kim signed a joint statement that contained a repeat of past vows to work toward a denuclearised Korean Peninsula. Lawmakers, analysts and allies have hailed the effort but questioned the substance of what was achieved.
Responding to a question, Trump said denuclearisation of Korean Peninsula does not mean that the nuclear umbrella that the United States has over South Korea is on the table of negotiations.
The IL-62 was one of three aircraft that flew to Singapore from North Korea's capital Pyongyang on Sunday. "Hope does not equal reality".
Tuesday's summit in Singapore was front page news on Wednesday, with full-page spreads of photos of Mr Kim and Mr Trump and details about the meeting.
North Korea typically heavily censors its local and foreign content, with events often not being reported until several days after, if at all. "So is a dangerously naive president".
There was news from the summit, Colbert said.
"No more rocket launches, nuclear testing or research!"
"We will be stopping the war games which will save us a tremendous amount of money".
Trump on Wednesday continued to tout his decision to suspend the military exercises as he returned from meeting North Korean leader Kim Jong Un in Singapore.
Backdrops of USA and North Korean flags, both red white and blue, were also prominent in the Rodong Sinmun, which has previously lashed the United States as a "gangster-like imperialist", and "cancer-like entity". "No longer - sleep well tonight!" the president wrote.
"I don't know exactly what the timing will be for our next conversation with the North Koreans", Pompeo said.
Pompeo said he was there when Trump talked about it with Kim, and the president "made very clear" that the condition for the freeze was that good-faith talks be ongoing.
The move, long requested by Pyongyang, has been seen as a major concession to North Korea and has left one former South Korean military leader "speechless". "I gave up nothing", Trump said. He told reporters he thinks he will know nearly immediately whether a deal can be made, saying: "I will know, just my touch, my feel".
At the start of his meeting with Kim, which began with a hand-shake, Trump said: "Working together we will get it taken care of..." "Moon, and then Trump, were quick to bite on North Korea's invitation for talks".
A pair of Democratic senators on Wednesday introduced an amendment to the annual defense policy bill that would stop President Trump from withdrawing USA forces from South Korea without the Pentagon's input. But no specifics of a future path were outlined. Typically, arms-control deals are verified by trained experts inspecting military and nuclear facilities.