Moon has maintained a two-track approach of seeking dialogue and sanctions, as North Korea has been advancing its nuclear and missile programs with the goal of developing a nuclear-tipped intercontinental ballistic missile capable of reaching the US mainland.
"The (Korean Peoples Army) is keeping a high alert, fully ready to contain the enemies".
North Korean state-run media said the country's military could strike the USA at any time and that neither Guam, Hawaii nor the U.S. mainland could avoid the "merciless strike".
The South Korean and U.S. militaries are in the midst of the annual Ulchi Freedom Guardian drills, which run until Aug 31. The North vows a strong military response to the exercise each year.
The US Pacific Command has confirmed the launches and added that "the first and third missiles failed in flight", while the second "appears to have blown up nearly immediately".
The rival Koreas recently saw their always testy relationship get worse after Pyongyang and US President Donald Trump traded warlike threats.
The 11-day exercise will involve 17,500 American troops and roughly 50,000 South Korean service members, according to the Pentagon and South Korea's Defense Ministry. It seems that North Korea is trying not to aggravate the situation.
Cheong Wa Dae refrained from issuing a statement condemning the North's act, which experts say reflects South Korea's hope that the current situation could set the tone for dialogue with the North.
A strong showing of top US military brass is on hand for the exercises.
Pyongyang fired three short-range ballistic missiles from the Kangwon province, the US Pacific Command said. However, Dunford last week emphasized that the military drills were "not now on the table as part of the negotiation at any level".
The launch is the first since a nocturnal test was carried out on July 28, in which an intercontinental ballistic missile was sacked into the Sea of Japan, provoking a new round of United Nations sanctions and rebukes from the global community.
Pyongyang launched its second intercontinental ballistic missile at the end of July and claimed that all the USA mainland was within its range.
South Korea's presidential office says North Korea has likely tested its 300-millimeter artillery rocket system in the latest launch detected off its eastern coast.