South Korea has worked with the United States to develop THAAD to help protect it in case of a North Korean missile attack.
Moon praised Modi for his leadership, saying India was becoming a global leader on various worldwide issues, including North Korea's nuclear ambitions. And if conditions are met I will go to Pyongyang.
Mr. Moon will have a hard diplomatic path to tread in his approach to the North, which dreams of a missile capable of delivering a nuclear warhead to the continental United States, and has vast artillery forces trained on Seoul.
Washington says the Terminal High Altitude Area Defence (Thaad) system will play a vital role in curbing the missile threat from Pyongyang, but Beijing says that the system's radar affects its security.
Many see Moon's manner as a refreshing break from his disgraced, jailed predecessor Park Geun-hye, whom critics saw as aloof and autocratic.
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.
China has already taken commercial retaliation against South Korean business interests on its soil, but will be hoping Moon follows through on his campaign pledge to review the missile system's deployment if elected.
South Korea and the USA began deploying the THAAD system in March and it has since become operational. First freeze North Korea's nuclear development, then engage with them economically before working towards the ultimate goal of denuclearization.
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.
Moon also said the two countries should "wisely resolve history-related issues", the official added.
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.
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.
South Korean President Moon Jae-in has expressed his gratitude to Indian Prime Minister Narendra Modi a day after the Indian leader tweeted in the Korean language to congratulate Moon on his election.