The US president and North Korean leader met in Singapore nearly a month ago for an unprecedented summit between sitting leaders of the two countries, which resulted in a general joint declaration that did not include a timetable or concrete commitments from North Korea on denuclearisation.
In practical terms, Pompeo mentioned only that officials from both sides would meet on July 12 as a working group to discuss the repatriation of the remains of some U.S. soldiers killed during the 1950-1953 Korean War.
It was not the first time Trump has lashed out at Beijing over his frustrations about the lack of progress in denuclearisation talks with Kim. Republican Senator Joni Ernst, a member of the Armed Services Committee, said joint military exercises with South Korea suspended to show goodwill toward North Korea should be resumed "soon" if talks sputter.
"We still cherish our good faith in President Trump".
However, the North Korean Foreign Ministry later released a lengthy statement that criticized the USA focus on nuclear weapons.
Speaking privately, USA officials suggested the harshly-worded North Korean reaction was a negotiating tactic.
CVID stands for complete, verifiable and irreversible dismantlement of North Korea's nuclear programme, an oft-cited demand by Washington for Pyongyang.
"The issues the USA side insisted on during the talks were the same cancerous ones that the past US administrations had insisted on", it added.
A letter from Kim to Trump was also delivered to Pompeo through Kim Yong-chol, a top North Korean party official.
He added that his two days of talks with senior North Korean officials had "made progress" and included a "detailed and substantive discussion about the next steps towards a fully verified and complete denuclearisation".
Unlike Pompeo, who dismissed North Korea's criticism and reiterated the importance of "maintaining maximum pressure" of sanctions against Pyongyang, Trump said China, North Korea's biggest diplomatic and economic supporting, could be influencing Kim.
North Korea hasn't said publicly what security assurances it would need to get rid of its nuclear weapons, but in the past they have included the withdrawal of the 28,500 US troops stationed in South Korea and an end to US-South Korean military drills. The accusation came after Pompeo visited Pyongyang and declared that the talks were productive.
Pompeo said sanctions would remain in place against North Korea, and be enforced "with great vigor", adding that progress alone does not change the sanctions.
As diplomatic engagement increases contact between the two Koreas and reduces hostility across the border, authorities may be anxious ordinary North Koreans might view the South favorably. "The miracle could be yours; it can be your miracle in North Korea as well".
Earlier in the day, Prime Minister Shinzo Abe stressed the importance of a comprehensive resolution of issues related to North Korea during his meeting with Pompeo.
Pompeo added that the USA and world powers would maintain economic sanctions against North Korea until full denuclearization was achieved.
Speaking privately, U.S. officials suggested the harshly-worded North Korean statement was a negotiating tactic.