"If the conditions shape up, I will go to Pyongyang [the North Korean capital]", Moon said.
"The reality is the majority of our people can not emotionally accept the comfort women agreement", Moon told Japanese Prime Minister Shinzo Abe Thursday.
During the 40-minute call, Xi stressed the importance of working together to achieve the common goal of denuclearizing the Korean peninsula - an aim dependent on resolving the thorny THAAD missile defense system issue.
"We should overcome the issue in a wise way, while making efforts to address the North's nuclear issue and advance bilateral relations separately", Moon was quoted as saying.
Theresa May and South Korea's new president have agreed the need for a "robust response" to Pyongyang's violations of United Nations resolutions.
Trump has raised the possibility of military action and pushed for tougher economic sanctions and new diplomatic measures to force North Korea to abandon its nuclear weapons program.More news: Here's how Resident Evil Revelations looks on PS4, Xbox One
This photo taken on February 6, 2017, shows the now-shuttered Kaesong Industrial Complex, a factory park that was jointly run by the two Koreas.
Regional experts have believed for months that North Korea is preparing for its sixth nuclear test.
The Chinese president noted that denuclearization of the Korean peninsula was also a goal for China, adding that the country supported peace and stability in the region.
Trump told Reuters in an interview last month major conflict with North Korea was possible but he would prefer a diplomatic outcome.
North Korea on Thursday urged Moon's government to end what it considers confrontational policies, including joint drills with the USA military.
Should Trump persist in that line, he could quickly sabotage both his North Korea initiative and bilateral relations with a vital American ally.More news: Miley has 'weird' friendship with Katy
Japanese officials have described the call as "positive and meaningful", with the two agreeing to cooperate closely to deal with North Korea.
Since it is anticipated he will take a milder approach to North Korea than his predecessor, he will have to first straighten things out with decision-makers in Washington, who until now have favoured imposing further isolation and sanctions.
"The South Korea-U.S. alliance is more important than at any other time given the growing uncertainties over the security situation of the Korean Peninsula", Moon said, according to a statement from the presidential office.
While South Korea, China and Japan all share worry about North Korea, ties between South Korea and China have been strained by South Korea's decision to install a United States anti-missile system in defence against the North.
Beijing has said the system would spy on its territory. China has vigorously opposed the deployment of a U.S. anti-missile system in South Korea, saying it threatens Chinese security and will do nothing to resolve tensions with North Korea.
China has been upset by the Terminal High-Altitude Area Defense system that was approved by Moon's conservative predecessor as a hedge against North Korea, placing Seoul in a hard spot between its closest military ally in Washington and its largest trading partner in Beijing. "We hope that the ROK side can pay attention to China's concerns and properly settle the issue", Geng said.More news: Angela Merkel's party wins vote in heartland of rivals in Germany
"President Moon said he understands China's interest in the Thaad deployment and its concerns, and said he hopes the two countries can swiftly get on with communication to further improve each other's understanding", Mr Yoon told a briefing.
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