Moon later spoke with Japanese Prime Minister Shinzo Abe and agreed to hold a bilateral meeting soon, Seoul and Tokyo said.
Xi told Moon that China has always upheld the denuclearization of the Korean peninsula and that the nuclear issue should be resolved through talks, which are in everyone's interests, according to the state television report.
Moon has been a critic of the hard-line stances that conservative governments in Seoul maintained against North Korea over the past decade and has called for sanctions and pressure against Pyongyang to be balanced with engagement efforts.
Ties between Seoul and Beijing have soured over the South's deployment of a controversial USA anti-missile system aimed at guarding against threats from the nuclear-armed North.
The two leaders agreed to exchange special envoys "at an early date" and Moon proposed sending a separate delegation to Beijing that will "exclusively discuss the THAAD and the North's nuclear issues", Yoon said.
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Those shared concerns could draw China, North Korea's most important global patron, and South Korea closer together, analysts say.
Moon Jae-in has taken the oath of office in Seoul hours after starting work as South Korea's new president.
China has pressured South Korea both economically and politically to abandon THAAD, which Beijing argues poses a threat to China's national security.
As president, Moon must find a way to coax an increasingly belligerent North Korea to ease its nuclear and missile threats while working with the United States, South Korea's main ally. Now, South Korea's new president says he is willing to meet with North Korean leader Kim Jong Un - if, of course, the conditions are right. And with 41,4% the liberal politician claimed a landslide victory on Tuesday, promising to be "the President of all Koreans". I think the key questions are between North Korea and the United States.
"I'd say we're at about dial setting five or six right now, with a strong call of countries all over the world to fully implement the UN Security Council resolutions regarding sanctions".
US prepares to ban laptops on flights from Europe
The carrier has suggested the current ban is discriminatory, and is paring capacity to the U.S.as the measures impact occupancy. Should one catch fire in the cargo area of a plane, there would be no way to access it in-flight to put out the flames.
Seoul is embroiled in a diplomatic dispute with her former colonial power Japan over its wartime history, however fellow U.S. ally Tokyo is also been targeted by the North.
Trump had said Seoul should pay $1 billion for the system, which has already been deployed, but Moon had said the deployment should be scrutinized or reviewed. Pyongyang has conducted its fifth nuclear test and a series of missile launches since the start of previous year, ratcheting up tension on the peninsula.
If Moon plans a "Sunshine Policy 2.0" - a revival of dialogue and economic aid to North Korea - he'll need to convince critics that a new economic relationship with the North will not lead to further nuclear arms development.
He's been critical of the decision to place THAAD, a US-built missile defense system, in the country's south.
Speaking to the Washington Post before the election, Mr Moon said himself that THAAD's deployment was undemocratic and that the timing "is not desirable".
Russian government releases photos of Oval Office meeting
In Washington, Tillerson made no comment on the Comey firing or on the substantive issues he would discuss with Lavrov. US intelligence agencies have asserted that Moscow meddled in the election to help Trump's chances of victory.