U.S. President Donald Trump, who spoke with Moon on Wednesday, this month opened the door to meeting North Korea's Kim Jong-un, saying he would be honoured to meet Kim under the right circumstances.
As well as clouding efforts to rein in North Korea's nuclear ambitions, the THAAD deployment has also led to recriminations from Beijing against South Korean companies.
Moon said at his inauguration Wednesday he is prepared to lead a major worldwide diplomatic effort to find a peaceful resolution to the tense security situation. "Moon had to be loyal to the policy line of engagement with North Korea, which is the identity his party represents".
China sees the deployment of the Terminal High Altitude Area Defense (THAAD) system as a threat to its own military capability and has slapped a series of measures against South Korean businesses seen as economic retaliation.
Chinese leader Xi Jinping called Moon Thursday to congratulate him on his electoral victory.
During his call with Japanese Prime Minster Shinzo Abe, the two leaders agreed that their countries must not let their hard history hamper co-operation in dealing with North Korea's nuclear programme, Moon's office said.
A liberal former human-rights lawyer, Mr Moon was sworn in a day earlier and said in his first speech as president that he would immediately address security tensions that have raised fears of war on the Korean peninsula. "The President said he had seen Modi's congratulatory message posted the night before in Korean language, and said he was grateful", Yoon Young-chan, the Chief Presidential Secretary for public relations, told a briefing.
Moon's attitude during the call appeared to significantly relieve senior bureaucrats in Japan who were concerned he would take a tougher stance and be reluctant to cooperate with Japan and the United States in dealing with North Korea's provocations.
Seoul and Washington began deploying the Thaad system in March and it has since become operational.
During their 25-minute conversation, Abe told Moon that he would like to "properly manage the bilateral relationship" in light of the accord.
Both sides should respect each other's major concerns and legitimate interests and try best to seek common ground and handle disputes properly, Xi said.
A high-ranking Japanese official, speaking on condition of anonymity, said Moon's willingness to meet Abe marks "a clear difference" from the attitude of former South Korean President Park Geun-hye.
Police officer who shot and killed Texas teen is fired
The teenager's brothers "witnessed firsthand" what happened, Merritt said. "Their young lives will be forever altered". Last year, Tulsa, Oklahoma police officer Betty Shelby shot and killed Terence Crutcher in the middle of a roadway.