Kong arrived in Washington earlier in the day on a mission to deliver Moon's message to Trump and lay the foundations for the first summit between the two leaders. The two countries agreed to hold a summit between Moon and Trump in Washington in late June.
South Korea's Defense Ministry said more analysis was needed to verify the North's claim on the rocket's technological features.
North Korea carried out another missile test Sunday and, unlike the test last month, this one was a success.
Moon asked Xi to personally look into ways to resolve the issue, Yonhap said.
This may be unacceptable to China, which argues THAAD is part of a U.S. effort to contain its growing military power and spy on activity within China using the missile system's powerful radar. Among other participants in the session were Vice President Mike Pence, National Security Adviser H.R. McMaster and Trump's son-in-law and senior adviser, Jared Kushner. North Korea's testing of the new missile system may make it more hard for Moon to follow along the path of reconciliation, However, in his first key appointments Moon appointed supporters of the earlier Sunshine Policy of improving ties with the North, to the positions of prime minister and head of intelligence.
Moon's messengers to China and Japan, senior Democratic Party of Korea lawmakers Moon Hee-sang and Lee Hae-chan, are now in their respective mission countries. His envoy for Russian Federation will leave next week. The liberal president also seeks parliamentary approval for the ongoing THAAD stationing, for which Trump has called for Seoul to pay $1 billion.
"President Trump talked largely about the big picture and stressed that we can achieve an outcome through the strong unity of the alliance and worldwide cooperation", Hong said.
Countries must decide whether they support North Korea or those opposed to its nuclear and missile programs, U.S. Ambassador the United Nations Nikki Haley said on Tuesday, vowing to "call out" states backing Pyongyang.
South Korea's Ministry of Unification (MOU) on Friday said it's "not desirable" for the government to comment on the KCNA editorial.
Moon won an election last week campaigning on a more moderate approach towards the North and said after taking office that he wants to pursue dialogue as well as pressure. In any case, he said, such a strike would likely "create a mushroom cloud over the Korean Peninsula".
Although Moon says he wants to return to a more realistic and open relationship with Pyongyang, he has to bear in mind the current United Nations sanctions, as well as the unpredictable response of Trump, who has been flexing his military muscles in Syria and Afghanistan.
While KCNA claims are not given much credence, nuclear expert Mira Rapp-Hooper of the Center for a New American Security, told Alex Ward of Vox that "this new missile suggests that [North Korea's] programs are advancing quickly" and a nuclear-tipped ICBM capable of reaching the USA mainland "may be only a year or so away".
South Korean envoy Moon Hee-sang (left) shakes hands with Japanese Prime Minister Shinzo Abe in a meeting in Tokyo, Japan on Thursday.
They also discussed the 2015 bilateral agreement on the issue of Korean "comfort women" who were forced to provide sex for wartime Japanese soldiers.
"This is the desire of our two peoples but also our governments".
"The keyword in the president's letter is that let's meet often and exchange often", the lawmaker told reporters.