President Moon Jae-in on Thursday issued a stern warning after North Korea's new missile test, saying he will never "stand back or compromise" on national security and people's safety.
The short range missiles flew for some 200 kilometres (124 miles) at an altitude of two kilometres before falling into the Sea of Japan, the ministry added.
Thursday's launches are the North's fifth round of tests -- three ballistic missile launches, a surface-to-air missile and now the cruise missiles - since the South's new president Moon Jae-in took power in early May.
This put China in line with new United Nations sanctions on Pyongyang after its nuclear test and rocket launch past year.
Moon ordered foreign affairs and security-related ministries to take measures in response to the North's latest provocation together with the worldwide community.
"It is incumbent upon us to assume that North Korea today can range the United States with an ICBM carrying a nuclear warhead", Vice Admiral James Syring from the U.S. Department of Defense, told a congressional hearing.
The UN Security Council last Friday unanimously adopted a US-drafted resolution imposing new targeted sanctions on a handful of North Korean officials and entities, in response to the recent tests.
Last week, North Korea fired a short-range ballistic missile that also landed in waters between South Korea and Japan.
North Korea described the latest United Nations sanctions as "mean" and warned they would not stop its missile and nuclear weapons programmes.
In 2016, the North's sole major ally China banned exports to the country of jet fuel and other oil products used to make rocket fuel.
It also comes a day after South Korean President Moon Jae-in formally said he would halt the deployment of a controversial US missile-defense system in South Korea while the government conducts an environmental assessment of the site in southern South Korea.
The USS Cheyenne, a Los Angeles-class nuclear-powered submarine, entered the port of Busan in South Korea on June 6, joining the USS Michigan, an Ohio-class nuclear-powered submarine, that arrived in port in late April. Japanese Foreign Minister Fumio Kishida said after this morning's launch that Tokyo has not detected any "flying objects" that headed toward Japan or landed inside the country's maritime economic zone.
The launch, said to be personally supervised by leader Kim, is the third test to be carried out in three weeks and comes amid growing tensions with the USA over its weapons programme.
The North says it needs nuclear weapons to forestall the threat of a U.S. attack.