"China, too, pays great attention to the bilateral ties", Xi said in comments in front of reporters in the Great Hall of the People in Beijing.
Paul Haenle, a former White House national security council official who now directs the Carnegie-Tsinghua Centre for Global Policy in Beijing, said Moon's election highlights the importance of South Korea's role in resolving the issue.
The Chinese president told Mr Lee on Friday: "We're willing to work with South Korea to preserve the hard-won results, properly handle disputes, put China-South Korea relations back onto a normal track".
Xi's remarks came in a meeting with South Korean special envoy Lee Hae-chan, who was dispatched to Beijing by new President Moon Jae-in on a mission to reopen contacts and seek a way out of the current impasse that has hit South Korean businesses hard.
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Striking a defiant stance, he added: "You can't let the critics and the naysayers get in the way of your dreams". He said he would give the Federal Bureau of Investigation a week and then "if we need a subpoena, we'll do it".
"China is willing to enhance communication with the new government of the ROK [Republic of Korea] on these issues, firmly promote denuclearization of the Korean Peninsula and restart related dialogue at an early date", the Global Times quoted Xi as saying.
Lee said the ROK acknowledged that the deployment of THAAD has harmed ROK-China mutual trust and exchanges, and fully understands China's reasonable concern over the issue.
The American THAAD defense system was deployed in South Korea last month, in response to North Korean missile tests.
China has been infuriated by the US deployment of the THAAD system in South Korea, saying it was a threat to its security and would do nothing to ease tensions with Pyongyang.
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At the Pentagon, Defense Secretary Jim Mattis said the missile test showed North Korea isn't heeding cautions from the worldwide community.
There are signs of possible strains between Washington and Seoul, after Trump said the South Koreans should pay for Thaad and warned he might scrap a trade deal.
Wang on Thursday reiterated calls for its dismantling.
"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", Wang told Seoul's envoy to China, Lee Hae-chan.
Since Moon Jae-in took office on May 10, signs have emerged that Beijing and Seoul are seeking to reconcile their differences and fix damaged relations caused by the THAAD dispute.
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Moon, for his part, in the run up to him winning the presidential election in South Korea said he would look to renegotiate and revise the 2015 agreement inked between both countries.