Pyongyang has carried out multiple launches since Moon - who backs engagement with the North but also stresses the need for sanctions - was elected in May.
He also urged Xi and Russian President Vladimir Putin to play a "constructive" role in dealing with North Korea.
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North Korean leader Kim Jong-un.
The launch is the sixth such test since Moon Jae-in was named South Korean president on May 10th.
China's UN Ambassador Liu Jieyi said that Beijing would push for the US and South Korea to halt military exercises on the Korean Peninsula in exchange for North Korea suspending its nuclear and ballistic missile programmes.
The US president is pressuring China, Japan and South Korea to take the next step.More news: Japan-EU trade pact continues to elude over auto, dairy tariffs
North Korea has a reliable arsenal of shorter-range missiles, but is still trying to flawless its longer-range missiles.
The launch appeared to be North Korea's most successful missile test yet. Trump had been pinning his hopes on China - North Korea's main diplomatic ally - to bring pressure to bear on Pyongyang, but declared last week that their efforts had failed. "Perhaps China will put a heavy move on North Korea and end this nonsense once and for all", he wrote on Twitter.
The U.S military says it tracked a North Korean missile for 37 minutes before it landed in the Sea of Japan.
A South Korean soldier watches a television news showing file footage of a North Korean missile launch on Tuesday.. More news: To Cut A Long Story Short… Tony Hadley quits Spandau Ballet
Sunday's phone call was characterized by the White House as Trump discussing the "growing threat" of North Korea's nuclear weapons program, while the Chinese government said the call signaled that the two countries' relationship was being "affected by some negative factors".
China's United Nations ambassador, Liu Jieyi, earlier told a news conference at United Nations headquarters that tensions between North Korea and the West are high "and we would certainly like to see a de-escalation".
And recent US naval maneuvers into areas China claims as its territorial waters have drawn sharp rebukes from Xi's government. North Korean state TV broke in with the announcement with a triumphant anchor declaring, "Our intercontinental ballistic rocket can reach anywhere in this world, and we can end America's nuclear threat and bring peace to the Korean peninsula".More news: US Carries Out Drone Strike Against Shabab Militants in Somalia
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