Greeting South Korean presidential envoy Lee Hae-Chan in Beijing, Foreign Minister Wang Yi said bilateral relations have made immense progress over the years.
"But this year we've had some undeserved setbacks," Wang said, likely in a veiled reference to the Terminal High Altitude Area Defence (THAAD) system that became operational earlier this month.
"We hope the new government will correct the problems that we have encountered and take effective measures and positions as soon as possible to remove the obstacles that have been placed on the road to good relations between our two countries."
Ties between Seoul and Beijing soured before Moon's election over the deployment of THAAD, which is aimed at guarding against threats from nuclear-armed North Korea. China sees THAAD as a threat to the regional security balance.
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Left-leaning Moon and President Xi Jinping spoke on the phone last week and both agreed that denuclearising North Korea was a "common goal" between them, Moon's spokesman said.
"We believe South Korea will bring clear measures to improve relations," Wang said.
For his part, Lee said Moon asked him "to express his thanks to President Xi for his message of congratulations after our election. He also asked me to come and engage in deep dialogue".
Moon, who took office yesterday, favours engagement with the North - whose key diplomatic backer is China - to bring it to the negotiating table over its nuclear and missile ambitions.
He has previously expressed ambivalence over the THAAD system and told Xi last week he was "well aware" of Chinese concerns about it, calling for bilateral talks to "increase understanding over the issue".
Tensions have been running high in the region, with Pyongyang launching what appeared to be its longest-range missile yet on Sunday.
US Ambassador to the UN Nikki Haley said the United States was working with China on a new sanctions resolution and warned that all countries must step up action against North Korea or face measures themselves.