Pompeo appeared alongside South Korean President Moon Jae-in, who said a second US-North Korea summit would provide a chance to take "a decisive step forward in the denuclearization and peace process on the Korean Peninsula".
China's public show of displeasure represented one of the strongest signs yet that the widening list of disputes between the United States and China could undermine their cooperation on North Korea.
Kim said the bilateral dialogue would continue to develop "based on the deep confidence between the two leaders", and expressed gratitude to Trump for making a honest effort to implement the agreement made at their June summit, KCNA said.
A meeting of top United States and Chinese diplomats in Beijing to discuss North Korean nuclear disarmament got off to a frosty start.
North Korea's official name is the Democratic People's Republic of Korea or DPRK.
"North Korea took some steps towards denuclearisation and the United States will face criticism from the global community if it continues to demand complete denuclearisation without any lifting of sanctions", said Yang Moo-jin, a professor at the University of North Korean Studies in Seoul.
The desire to welcome the leader of the Catholic church comes as Kim attempts to transform his image from paranoid head of a rogue state to young and dynamic world leader. But that wasn't an advance on comments Trump made last month in NY, when he said he wanted to meet Kim "very soon".
But unlike his last visit to Beijing in June, Pompeo did not have a meeting with Chinese President Xi Jinping.
The move signals a new step forward in Pyongyang's commitment to denuclearizing the Korean Peninsula.
Meanwhile, in Washington, foreign relations experts noted that with 90 percent of North Korea's exports going through China, Beijing is the one calling the shots. Last week, Vice President Mike Pence stepped up the USA pressure campaign against Beijing, going beyond the trade war by accusing China of both "malign" efforts to undermine President Donald Trump ahead of next month's congressional elections and of reckless military action in the South China Sea.
The Secretary of State added that South Korea has been an integral part of negotiations aimed at denuclearising North Korea, and he passed along Mr Trump's gratitude for the country's efforts.
Wang said the North Korean issue shows that Beijing and Washington "can and should increase communication and cooperation".
Yang said China and the USA must expand political cooperation to achieve mutual aims.
The mystery for analysts and observers remains how much more may be going on behind the scenes than USA officials are admitting publicly.
"I know that you would like to discuss the North Korea issue and other relational issues with me on this visit", Wang said.
"But with respect to our relationship with the Republic of Korea and Japan on this issue, I have found that we are in lockstep on the most important issues and how to approach them", Pompeo said. "If that isn't happening, then it's a really interesting question of what even the point of a second summit would be".