As he took the oath of office Wednesday, Moon said he was open to visiting Pyongyang under the right conditions to discuss its nuclear programme. He asked them to help in curbing North Korea's nuclear programme and both promised to.
Mr Moon, of the liberal Democratic Party, is widely expected to improve long-strained ties with the North.
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.
But analysts said the new South Korean president is likely to be constrained and more pragmatic in office, instead of making a U-turn on current policies towards North Korea.
The call with Xi was Moon's second telephone conversation as president with a key global leader, following one Wednesday with U.S. President Donald Trump.
China was willing to keep working hard with all parties, including South Korea, for the peace and prosperity of the Korean peninsula, he said.
He has also made it amply clear he does not support the deployment of U.S. Terminal High Altitude Area Defense (THAAD), on his country's borders for which Trump has demanded South Korea pay $1 billion.
The new South Korean president faces the daunting task of finding a way to restore relations without upsetting global partners such as the US, given Pyongyang's self-description as a nuclear weapon state.
Yoon said the initiative was mentioned during a 40-minute phone call yesterday, the first between Moon and China's President Xi Jinping.
"In South Korea, what defines you as a conservative or progressive candidate comes down to your policy position on foreign policy", James Kim, an global relations expert at the Asan Institute for Policy Studies in Seoul, told Sputnik.
Despite its anger at North Korea's repeated nuclear and missile tests, China remains the isolated state's most important economic and diplomatic backer even with Beijing signing up for tough United Nations sanctions against Pyongyang.
The deployment of THAAD was agreed past year by South Korea's previous administration after North Korea conducted a long-range rocket launch that put an object into space.
"How to respond to North Korea ... is an urgent issue". He also calls for the United States to bring back tactical nuclear weapons to South Korea after withdrawing them in the 1990s.
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.