Haley said Pompeo had delivered "solid" US demands to North Korea and that Washington would not weaken those or ease sanctions on Pyongyang.
The dismantlement has been made as a follow-up to North Korean leader Kim Jong Un's pledge at the June 12 summit with U.S. President Donald Trump to dismantle one of the missile test sites.
The two sides vowed at that time to work towards North Korea's denuclearisation but have struggled to reach a deal to meet that goal, with the United States insisting that sanctions pressure must be maintained during negotiations. Among the agreements was holding another inter-Korean summit in the fall in Pyongyang.
North Korea went ahead with the return of the remains of some US soldiers killed in the 1950-53 Korean war in a goodwill measure aimed at breaking down mistrust between the countries, it said.
USA officials, according to North Korea, "are making baseless allegations against us and making desperate attempts at intensifying the worldwide sanctions", against what they believe to be Trump's intentions to better relations between the two countries.
Still, North Korea said it remains steadfast in its commitment to building trust and implementing in good faith the joint statement step by step.
"I can tell you we continue to have conversations virtually every day, every other day or so with the North Koreans", Heather Nauert, U.S. State Department spokeswoman, said Thursday "When I say 'conversations, ' that can be by phone, that can be my message, that can be by email". "It's just North Korea that has not taken the steps we feel are necessary to denuclearize".
With such moves, "one can not expect any progress in the implementation of North Korea-US joint statement including the denuclearization, and furthermore, there is no guarantee that the hard-won atmosphere of stability on the Korean Peninsula will continue", said the spokesperson.
North Korea's foreign ministry said on Thursday it had stopped missile and nuclear tests and dismantled "the nuclear test ground", yet the United States still insisted on "denuclearisation first".
The North apparently wants it to ensure the security of its regime.
North Korea has condemned the USA for placing fresh sanctions on it and called on the country to respond to its efforts to improve bilateral ties.
But a recent United Nations report showed Pyongyang was continuing with its nuclear and missile programmes and evading sanctions through ship-to-ship oil transfers.