South Korea-China relations soured this year following China's protest against South Korea agreeing to deploy USA -supplied THAAD missile defense system on its territory.
He called on the two sides to synergize development strategies, take advantage of their complementarity and strengthen mutually beneficial cooperation in such areas as economic and trade, finance, manufacturing and environmental protection.
The meeting, the first of its kind, was held on the sidelines of the Association of Southeast Asian Nations (Asean) forum in Manila.
For his part, Moon said that bilateral ties are now standing at a new starting point.
It provided no details but China has been seeking to get relations with Japan and South Korea back on track after disputes over how to rein in North Korea's nuclear and missile programmes, and, in Japan's case, over the two countries' sensitive wartime history.
(Chinese) "China, South Korea relations and the situation on the Korean peninsula are at a pivotal stage".
Also on Saturday, the US and South Korea launched a joint naval drill in a show of strength against the North's leader Kim Jong-un. "I believe we have created a chance to quickly normalize the countries' relationship through my talks with President Xi Jinping".
Speaking to reporters in the Philippines, Moon said that if North Korea agreed to hold talks, negotiations could be held with all options open.
Better relations with China will help the nation withstand potential rough economic conditions next year, South Korean Vice Finance Minister Ko Hyoung-kwon told Bloomberg News in an interview last week.
"Prime Minister [Li] said the countries will inevitably face sensitive issues as the China-South Korea relations develop, but that the development of practical cooperation between China and South Korea is very bright", Yoon told a press briefing.
Moon made the remarks at the annual East Asia Summit (EAS), attended by the leaders of 17 other countries, including China, Japan, Russia and the United States.