Moon was sworn in as president of South Korea on Wednesday, a day after he was declared the victor of the election.
In a sign of Washington's growing concern about the North, the Central Intelligence Agency announced Wednesday its establishment of an integrated "Korea Mission Center".
"I will quickly move to solve the crisis in national security".
Katina Adams, a spokeswoman for the U.S. State Department, said Washington had worked closely with Seoul on North Korea and would continue to do so.
Moon also has spoken of reconsidering deployment of the US missile defense system known as THAAD that the last government rushed into service.
The waning years of recently ousted South Korean president Park Geun-hye's administration saw Seoul's relationship with Beijing deteriorate as dramatically as did Park's reputation. But challenging Washington over THAAD might be hard for Moon. But a WSJ op-ed by Michael Breen said Moon's approach is likely to be more realistic than the "sunshine policy". Moon also said he would review the THAAD deployment.
He told Xi the ultimate goal of sanctions was to persuade North Korea to engage in dialogue about abolishing its nuclear program.
Presidents Moon and Xi began their conversation at around noon and spoke for about 40 minutes.
"President Trump said he looks forward to working with President Moon and invited him to visit Washington at an early date".
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Taking the oath of office in Seoul on Wednesday, Moon said he will further bolster the alliance and "immediately fly to Washington if necessary" for the sake of peace on the Korean Peninsula.
The U.S. and North Korea aren't now involved in any diplomacy.
"The resolution of the North Korean nuclear issue must be comprehensive and sequential, with pressure and sanctions used in parallel with negotiations", Moon's spokesman, Yoon Young-chan, quoted Moon as telling Xi.
During Thursday's call, Xi reaffirmed China's opposition to the THAAD deployment, Moon's office said.
China says the Terminal High Altitude Area Defence (Thaad) undermines its security, as its powerful radar can probe deep into its territory.
The US military has carried out a show of force with the South Korean and Japanese armed forces in recent weeks.
Moon also appealed to Beijing to stop its apparent economic retaliation against South Korean businesses over THAAD.
North Korea's heightened threat could change Moon's calculus once in power. "We're going to see what happens", Trump added, according to a transcript released yesterday. Instead, he only told Abe that there are "cautious opinions" circulating in public about the accord, which was signed to put the issue of comfort women to rest "finally and irreversibly", the official said. Rival versions of events fuel territorial disputes, bilateral mistrust and diplomatic rifts.
Scrapping the textbooks was one of Mr Moon's campaign pledges.