The series of tweets came a day after the conclusion of trade talks in Washington, DC, between lower level Chinese and USA trade officials.
According to CNN, Pompeo was planning on visiting Pyongyang next week for his fourth trip there.
Trump went on to blast China, accusing Beijing of failing to facilitate the denuclearization process because of trade disputes with the U.S.
Trump's decision to call off Pompeo's trip is clearly a frustrating development for South Korean President Moon Jae-in, who continues to push for inter-Korean engagement. Moon is scheduled to visit Pyongyang in September for his third summit with Kim this year.
Mr Pompeo might still make another trip though.
At a news conference announcing the appointment, Biegun reiterated the White House's stance that this process will have to begin with Kim handing over his nukes.
USA negotiators have struggled in recent weeks over a North Korean demand for the United States to declare an end to the Korean War before the North makes any concessions on denuclearisation.
A Rocket has not been launched by North Korea in 9 months. The conflict stopped with the signing of an armistice rather than a peace treaty, meaning the war is not technically over.
Kelly Magsamen a former US deputy assistant secretary of defense for Asian affairs, said Trump was undermining his leverage with Kim as well as that of Pompeo and his new envoy. Biegun will be tasked with handling day-to-day negotiations with the North over dismantling its nuclear weapons.
"Those hopes are dashed, at least for now", he added.
Trump's tweets followed a report issued by the International Atomic Energy Agency this week outlining "grave concern" about the North's nuclear programme. The North has been demanding that the United States ease or lift the sanctions that are crippling its economy.
He has said, however, that a visit is likely to go ahead in the future. "Much of those conversations you know I will not be detailing for you here from this podium", she said. "We've been very upfront about how this will take some time".
"It's fine to not send the Secretary due to lack of progress, but don't then also talk about how you are eager to meet with KJU and how China is thwarting you", she tweeted. I look forward to seeing him soon!'
Negotiations have all but deadlocked since the June summit in Singapore.
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