Moon's predecessor, Park Geun-hye, who was impeached and ousted as president, had agreed to the deployment of THAAD, saying that it was needed to protect South Korea against a growing ballistic-missile threat from North Korea.
Moon later spoke with Japanese Prime Minister Shinzo Abe and agreed to hold a bilateral meeting soon, Seoul and Tokyo said.
They came as North Korea's ambassador to the United Kingdom told Sky News his country will go ahead with its sixth nuclear test at a time and place of its leader's choosing.
Mr Moon told Mr Abe that most Koreans could not accept the agreement, according to the Blue House, while Japan's top government spokesman Yoshihide Suga said Mr Abe told him it was "extremely important" to implement it.
USA officials have said they see no value in resuming worldwide talks with North Korea under current circumstances and that Pyongyang must make clear it is committed to denuclearization. North Korea continued its progress in becoming a nuclear state.
But until Thursday, South Korea had not been invited.
The North's state-run propaganda Web site Uriminzokkiri claimed that North Korea policies that are hostile to fellow countrymen and intensify confrontation should be fundamentally eliminated.
Mr Moon is making a gesture to mend ties with China, but it does not necessarily mean he will revoke the missile system, said observers.More news: With new president, new faces for French parliament
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In the first direct contact between the South Korean and Chinese leaders, Mr Xi explained Beijing's position, said Mr Yoon, the South Korean presidential spokesman, without elaborating.
"President Moon said he understands China's interest in the THAAD deployment and its concerns, and said he hopes the two countries can swiftly get on with communication to further improve each other's understanding", Yoon said.
Seoul and Washington began deploying the Thaad system in March and it has since become operational.
Xi told Moon that Seoul and Beijing should respect each other's concerns, set aside their differences, seek common ground and handle disputes appropriately, China's foreign ministry said in a statement.
Yoon said that President Moon highly evaluated India's participation in worldwide sanctions against the North.
China has denied it is retaliating against South Korean businesses.
Unless North Korea stops the development of its nuclear weapons and starts the process of denuclearization, there's little room for Moon to lift existing economic sanctions and initiate engagement with its neighbor in the north, including reopening the Kaesong Industrial Complex that the previous administration said was funneling hard currency to the regime in Pyongyang.