Chinese Foreign Minister Wang Yi shake hands with Secretary of State Mike Pompeo before a meeting in Beijing on Monday. China and the United States are at odds over trade and Beijing's militarization of islands it claims in the South China Sea.
Russian Federation is drawing up plans to host a meeting between President Vladimir Putin and North Korean leader Kim Jong Un in Moscow, according to the Kremlin.
Trump and Kim held an historic first summit in Singapore in June.
A meeting of top USA and Chinese diplomats in Beijing to discuss North Korean nuclear disarmament has got off to a frosty start.
Pompeo told reporters in Pyongyang the two "had a great, great visit" and that Trump sent his regards. Chinese leader Xi Jinping is also expected to travel to North Korea.
Moon also said the North will "permanently dismantle" its missile engine testing site and launch platform in the northwestern town of Tongchang-ri in the presence of experts from "concerned countries".
The two diplomats had warmer words regarding efforts to curb North Korea's nuclear ambitions. It came amid expectations that his meeting with leader Kim could provide momentum to get the denuclearization process going again after a monthslong stalemate over how to rid the North of its nuclear weapons program.More news: Man City owner Sheik Mansour nearly bought Newcastle United
A senior USA official said getting a deal on denuclearisation is going to be a "long haul" in the immediate aftermath of Mr Pompeo's fourth visit to the isolated state's capital city.
After a previous visit to Pyongyang in July, Pompeo had said the two foes made progress on key issues - but within hours of his departure the North condemned "gangster-like" demands from the United States, raising questions over how much the two sides really saw eye to eye.
A senior State Department official said, despite their differences, the USA still expected China to cooperate on efforts to denuclearize North Korea.
North Korea only invited a foreign press corps to witness the explosion of the nuclear test site in May.
A stalemate followed with the two countries struggling to agree over the exact terms of the vaguely worded deal secured in Singapore, with the U.S. calling for a "final, fully verified denuclearisation" of North Korea, while Pyongyang says more trust is needed.
After Seoul, Pompeo ends his trip Monday in China, North Korea's political and economic lifeline.
Pompeo did not specify when the summit will be or if Pyongyang has been ruled out as a location.
USA officials have thus far said the penalties will remain in place until the North's denuclearization is fully verified.