The launches come amid ongoing USA wargames in South Korea.
The launches come as tens of thousands of South Korean and United States troops take part in joint military drills in the South, which Pyongyang views as a highly provocative rehearsal for an invasion of its own territory.
Kim says North Korea's large-sized artillery rockets blur the boundaries between artillery systems and ballistic missiles because they create their own thrust and are guided during delivery. In July, it launched an intercontinental ballistic missile, which North Korea claims could reach "anywhere in the world".
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Three North Korea short-range ballistic missiles failed on Saturday, U.S. military officials said, which, if true, would be a temporary setback to Pyongyangs rapid nuclear and missile expansion.
None of the missiles, launched from near Kittaeryong in the North, had posed a threat to either North America or the US Pacific territory of Guam, the spokesman added. "We place confidence in our US Department of Defense capabilities and continue open communications with our federal and military partners". It said earlier that the third missile appears to have blown up immediately.
"Our military is closely monitoring for North Korean additional provocation and strengthened surveillance and security postures and maintaining readiness postures", the South Korean release said.
Tillerson called North Korea's "restraint" pleasing and said it could open a pathway for dialogue in the near future.
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But earlier this week the rhetoric appeared to be cooling - at least on the American side - as Trump expressed optimism about North Korea on Tuesday, saying of leader Kim Jong Un, "I respect the fact that he is starting to respect us".
Throughout the year, North Korea has conducted a series of ballistic missile tests.
"The reality vividly shows that the US ambition for stifling [North Korea] remains unchanged no matter how much water may flow under the bridge and the puppet group's ambition for invading the north remains unchanged", the state-run Korean Central News Agency reported.
Xi made the remarks in a congratulatory message sent to Moon on the 25th anniversary of the establishment of China-South Korea diplomatic relations, Xinhua news agency reported.
North Korea launches 3 short-range ballistic missiles into sea
The North has often tested missiles with similar scope, but the use of a multiple-tube launcher shows an advance in capability. The first and third missiles launched at 6:49 a.m. and 7:19 a.m.