The Moon-Xi meeting came after months of dispute caused by China's protest against the deployment of the THAAD missile defense system in South Korea.
South Korea and the United States on Saturday kicked off a joint naval exercise in the Sea of Japan involving three USA aircraft carriers amid heightened tensions on the Korean Peninsula.
Their navies plan to begin the four-day drill, which will involve the three flattops - USS Ronald Reagan, USS Nimitz and USS Theodore Roosevelt - in the East Sea on Saturday, according to the Joint Chiefs of Staff (JCS). The Aegis technology refers to missile tracking and guidance.
On North Korea's nuclear and missile development issue, the two leaders agreed the need to stably manage the current security situation on the Korean Peninsula.
The last time such drills were held was during the Valiant Shield exercises in 2006 and 2007, which took place off the coast of the USA territory of Guam, which hosts two US military bases and is on the North Korean radar for a potential missile strike. The U.S. carriers will also participate in separate exercises with three Japanese destroyers on Sunday, according to Japan's Maritime Self-Defense Force.
The U.S. Navy's previous training operation involving three carriers was in the vicinity of Guam in the Western Pacific in 2007 during the Valiant Shield exercise.
The United States has been sending its strategic assets, also including long-range bombers, to the region more frequently for patrols or drills amid accelerating North Korean efforts to expand its nuclear weapons program.
It has repeatedly threatened to launch ballistic missiles into the waters around the USA territory of Guam.
President Trump's exchange of threats and insults with Pyongyang has done nothing to curb regional tensions and with South Korea and China suited either side of the hermit state, it is in their interests not to push for military action.
The Chinese leader also encouraged South Korea to resume dialogue with North Korea and re-engage with them for reconciliation and de-nuclearisation.