Moon, who predicated his campaign on engaging, not isolating Pyongyang, now must react to North Korean claims that the intermediate-range ballistic missile can carry a heavy nuclear warhead.
North Korean propaganda must be considered with wariness - Pyongyang has threatened for decades to reduce Seoul to a "sea of fire", for instance - but Monday's claim, if confirmed, would mark another big advance toward the North's goal of fielding a nuclear-tipped missile capable of reaching the USA mainland.
Describing the missile launch as a "grave provocative act that damages the peace and security of the region and the worldwide community", Inada relayed to her counterpart Japan's intention to beef up its cooperation with the new South Korean government under President Moon Jae In.
The U.N. Security Council is due to meet Tuesday to discuss North Korea's latest missile, which the White House said should "serve as a call for all nations to implement far stronger sanctions" against Pyongyang.
In a unanimous statement backed by China, the council stressed the importance of North Korea "immediately showing honest commitment to denuclearisation through concrete action".
"There's a lot of sanctions left that we can start to do, whether it's with oil, whether it's with energy, whether it's with their maritime ships, exports", US Ambassador Nikki Haley told ABC television's "This Week". "But its overwhelming emphasis is diplomatic and economic sanctions".
North Korea's official Korean Central News Agency called the missile a "new ground-to-ground medium long-range strategic ballistic rocket", and said the "Hwasong-12" was "capable of carrying a large, heavy nuclear warhead".
On Monday, North Korean state media showed photos of Kim Jong Un laughing and hugging his rocket scientists after the launch, which he personally oversaw, the report said.
The country's leader, Kim Jong Un, supervised the launch of the Hwasong-12 missile that reached an altitude of 2,111.5 kilometers (1,312 miles) and flew 787 kilometers (489 miles), KCNA said.
That signalled a new phase in applying sanctions that curb exports of coal from North Korea, impose severe restrictions on banking and ban sales of luxury goods and equipment that could be of use to the military.
What has North Korea been saying?However, Russia said it fell 310 miles (500 kilometers) from its coast.
Haley said Russian Federation also is "concerned", especially since the missile hit relatively close to home. He has also vowed to prevent North Korea from being able to hit the United States with a nuclear missile, a capability experts say Pyongyang could have some time after 2020.
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There are doubts whether the North can miniaturise a nuclear weapon sufficiently to fit it onto a missile nose cone, and no proof it has mastered the re-entry technology needed to ensure it survives returning into Earth's atmosphere.
"If the USA awkwardly attempts to provoke the DPRK, it will not escape from the biggest disaster in the history, Kim said, strongly warning the U.S. should not to disregard or misjudge the reality that its mainland and Pacific operation region are in the DPRK's sighting range for strike and that it has all powerful means for retaliatory strike", KCNA said.
South Korea said on Monday it will seek to strengthen allegiances with its allies as tensions mount in the wake of the launch.
"As South Korea's diplomatic situation matures, North Korea should also show a more mature attitude, not a childish one, and contribute to (establishing a better) diplomatic relationship".
In Seoul, some citizens expressed frustration.
"It's good to keep the door for conversation open".
While Trump has said he'd be "honored" to talk Kim under favorable conditions, Haley seemed to rule out the possibility.
US officials reported that the missile landed 60 miles from the Russian city of Vladivostok.
A press statement issued by the council late Monday expresses "utmost concern" at what it calls North Korea's "highly destabilizing behavior" and demands that Pyongyang conduct no further nuclear or ballistic missile tests.
What's worrying to the United States, among other countries, is that if this missile were fired at a different trajectory, it could have reached the US Andersen Air Force Base in Guam, according to aerospace engineer John Schilling's 38 North blog, which is published by the US Korea Institute at Johns Hopkins University.
KCNA cited Kim as saying the North would never succumb to what it called the "highly ridiculous" U.S. strategy of "militarily browbeating only weak countries and nations which have no nukes".
While North Korean provocations played a part in the election, domestic dynamics took on perhaps even a bigger role. The USS Carl Vinson, an aircraft carrier, is also engaging with South Korean navy ships in waters off the Korean Peninsula, according to Seoul's Defense Ministry.