In a public ceremony after a summit in Tokyo, Japanese Prime Minister Shinzo Abe and Chinese Premier Li Keqiang oversaw the signing of a pact to set up within 30 days a hotline for senior defence officials to communicate during incidents involving each others' naval vessels or military aircraft.
President Donald Trump is promising "quite a scene" when three Korean Americans detained in North Korea return to the mainland USA after more than a year in prison.
North Korean leader Kim Jong Un met Mr Moon on April 27 and Chinese President Xi Jinping earlier this week, in a surprise visit to the Chinese coastal city of Dalian.
China and Japan, in particular, have differences over how best to achieve North Korea's nuclear disarmament.
Li and Moon both urged Abe to meet with Kim while reporters were in the room, a possible attempt to stimulate a review of the Japanese position of using only pressure to change North Korean policy.
Leaders of the three Asian powers, whose ties have been strained by territorial and historical disputes, also touched on economics in the face of US trade pressure on China and Japan.
Currently, China-Japan ties are showing a momentum of improvement and standing at the crossroads of returning to normal track, he said. The summits, which started in 2008, are supposed to be held annually, but Wednesday's was the first since November 2015.
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Chinese Premier Li Keqiang said at the same news conference he supported the idea of dialogue between Japan and North Korea.
Li called on both sides to cherish the hard-won momentum of improvement in bilateral relations, carry forward the spirit of the treaty, and promote new progress in their ties, in a bid to provide stable and positive expectations for the two peoples as well as the global community.
For one, it would be extremely hard for Abe to hold a summit with North Korea in the absence of any progress in resolving the issue of Japanese nationals abducted by North Korea decades ago.
Japan's leader was to hold talks separately with Mr Moon and Mr Li later.
Mr Moon is to leave Japan after half a day.
Sun Cheng, a Japanese affairs expert at the China University of Political Science and Law, said while Li's visit was a good sign for bilateral ties, suspicions ran deep between the two sides.