Pentagon officials also plan to meet with North Koreans Thursday to discuss the return of remains of war dead, he said.
"We expected the US to bring constructive measures to build confidence in accordance with the spirit of the US-NK Summit", the statement carried by state-run news agency KCNA said.
"We did have very serious discussions on very important matters yesterday", Kim said. China is North Korea's traditional ally and main trading partner, and is key to maintaining sanctions on Pyongyang.
But while Pompeo on Saturday painted a positive picture of the follow-up talks, North Korean officials accused the United States of trying to unilaterally pressure their country into abandoning its nuclear programme.
Pompeo, however, said more talks were needed on both.
South Korean Minister of Foreign Affairs Kang Kyung-wha said that the North had balked at a written pledge for "complete, verifiable and irreversible denuclearization" for historical reasons, but stressed that the goal remained the same whether or not that exact phrase was used.
Speaking in a tweet on Saturday, the Morning Joe host shared an article from The Washington Post that said North Korea had referred to the U.S.as "gangster like" in comparison to Secretary of State Mike Pompeo's assessment that his two-day talks were "productive". "It can be your miracle in North Korea as well", Mr Pompeo said.
Pompeo has reportedly established a working group inside the State Department on ways to achieve denuclearization of North Korea, but that group does not include officials from the Pyongyang side, according to the U.S. Our expectations and hopes were so naive it could be called foolish'.
North Korea calls talks with the United States "regrettable" while Secretary of State Pompeo says the discussions were productive; former USA ambassador to the U.N. Bill Richardson weighs in on 'Sunday Morning Futures'.
"I am determined to achieve the commitment that President Trump made", Pompeo said.
The regime's belief that the weapons are needed to deter a United States attack dates back almost 70 years to the still-unresolved Korean War, and will take more than a handshake to dispel.
"Clearly, we see some posturing particularly from the North Korean side using the leverage that they have, especially in the lead-up to Trump's visit to NATO and his big summit with [Russian President] Vladimir Putin in the coming week", said Hilary Mann Leverett, a former White House official.
The statement was widely seen as a negotiating tactic to put the U.S. on the back foot as talks get underway. The first major follow through on a trade threat directed unilaterally at China coincided with Pompeo's meeting in North Korea last week, adding to speculation that China may be trying to leverage its position as the final guarantor of economic pressure on Pyongyang in trade talks with the US. Why should the North Koreans make concessions to one of Trump's aides given the president's record of undercutting them?'