Taking the oath of office in Seoul on Wednesday, Moon said he will further bolster the alliance and "immediately fly to Washington if necessary" for the sake of peace on the Korean Peninsula.
The deployment of the Thaad system was agreed on by Park's administration previous year after North Korea conducted a long-range rocket launch that put an object into space.
North Korea on Thursday urged Moon's government to end what it considers confrontational policies, including joint drills with the USA military.
Moon has taken a more conciliatory line with North Korea than his conservative predecessors and advocates engagement.
However, while Donald Trump has sought the help of countries such as Russia, China, Japan, as well as South Korea in dealing with Kim, Moon is intent on adopting a more lenient approach, Newsweek reports.
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. First freeze North Korea's nuclear development, then engage with them economically before before working towards the ultimate goal of denuclearization.
Stangarone also added that whatever global plans Moon has, the economic situation in South Korea and the fact that he was elected following an impeachment mean that domestic issues will constrain what he wants to do.
With only an acting president in place for several months, South Korea has found itself caught between the US and China on the diplomatic and economic front.
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Moon also spoke with Japanese Prime Minister Shinzo Abe on Thursday, with the two agreeing to cooperate closely on the North Korea issue. He is reportedly against the aggressive military measures Trump has threatened to deploy if North Korea does not back down from vigorously expanding its nuclear regime. Moon accepted the invitation at an "early date" but no specific time was set, according to a statement.
Mr Moon's position on Thaad is not yet completely clear - his comments have been ambivalent in the past.
The Terminal High-Altitude Area Defense (THAAD) system, which would intercept attacks from North Korea, became operational in South Korea last week.
Beijing has asked the deployment be canceled because of THAAD's powerful radar and regional surveillance capabilities.
Trump has also been calling for a renegotiation of the bilateral free trade agreement (FTA) and for Seoul to shoulder a larger cost of maintaining US troops in Korea and pay for a $1 billion antimissile system.
Moon came to power with a promise to review the system and he told Xi North Korea must cease making provocations before tension over the deployment could be resolved, officials said.
North Korea accused the USA and South Korean security agencies of planning a biochemical attack on leader Kim during April 15 celebrations in the North's capital of the anniversary of the birth of state founder Kim Il Sung.
During the 40-minute conversation, he also proposed sending a special delegation to Beijing that will "exclusively discuss the THAAD and the North's nuclear issues", Yoon said.
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