"South Korea alliance is more important than ever before", Moon said, according to Yonhap. But a WSJ op-ed by Michael Breen said Moon's approach is likely to be more realistic than the "sunshine policy".
The conversation is a sign of willingness to fix relations between the two countries.
The deployment of THAAD was agreed by former President Park Geun-hye's administration previous year.
Mr Moon's choice as head of the National Intelligence Service, Suh Hoon, backed a return to talks.
The winning candidate will be officially sworn in as South Korea's new president after the election commission finishes the vote count and declares the victor Wednesday morning.
South Korea's relationship with China has been tense in recent months due to the deployment of the USA missile defense system THAAD, which China sees as compromising its military interests. But challenging Washington over THAAD might be hard for Moon.
In his speech, Moon, 64, also pledged to sever what he described as the collusive ties between business and government that have plagued many of South Korea's family-run conglomerates, known as chaebol, and vowed to be incorruptible.
Moon said Pyongyang's nuclear issue should be addressed "comprehensively and gradually", not only with pressure but also through talks, because current worldwide sanctions are also aimed at guiding Kim's regime to return to dialogue, Yoon said. Trump has called for South Korea to pay the US $1 billion for a system the USA has always described as in America's vital security interests.
He will send a delegation to Beijing to discuss both North Korea and Thaad.
China was willing to keep working hard with all parties, including South Korea, for the peace and prosperity of the Korean peninsula, Xi said.
The election victory of Moon Jae-in in South Korea confronts Washington with a scenario it faced a decade-and-a-half ago, when differences on how to deal with Pyongyang fueled tension with an ally that hosts US forces.
South Korean President Moon Jae-in, third from left, walks with senior presidential secretaries at the presidential Blue House in Seoul, South Korea, Thursday, May 11, 2017.
Moon said he would send a special envoy to Russian Federation soon and Putin said he would welcome the envoy.
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.
The US military has carried out a show of force with the South Korean and Japanese armed forces in recent weeks. Chinese group tours to South Korea have also been canceled, while anti-Korean sentiment has proliferated online.
Moon also raised the issue of economic retaliation against South Korean firms in China, Yoon said.
Suh said Moon could go to Pyongyang if it was clear the visit would help resolve the North Korean nuclear crisis and ease tensions.
Japan has repeatedly insisted the agreement is irreversible despite the protests of now-elderly former "comfort women". He has suggested revisiting a deal settling the historical dispute related to abuses suffered by Korean women in Japanese military brothels during World War II. Moon has called for a renegotiation of the pact.
It remains to be seen whether Seoul's new government might reverse the deployment following a re-think promised by Moon's Democratic Party. South Korea plays a crucial role in regional stability, it said. Together, they host tens of thousands of USA troops.