"Sharing the view that South Korea needs to bolster its defense capabilities to counter North Korea's provocations and threats, the two leaders agreed in principle to revise the missile guidelines to a level that the South Korean side desires", read a statement from President Moon's office, quoted in the country's news agency Yonhap.
Pyongyang issued a statement on Sunday afternoon and claimed it has successfully conducted a test of a hydrogen bomb mountable on an intercontinental ballistic missile.
The leaders of the United States and South Korea on Friday reaffirmed the need to bring Pyongyang back to the negotiating table by applying maximum sanctions and pressure, according to the office of President Moon Jae-in.
In Seoul, the presidential Blue House spokesman confirmed that U.S. President Donald Trump and his South Korean counterpart Moon Jae-in agreed to enhance the country's deterrence against North Korea by boosting its missile capabilities.
"I can not tell you about our forthcoming response to North Korea, but we have just completely agreed on it", Abe told reporters at his office after his latest call with Trump on Thursday.
The U.S. Chamber of Commerce said in an email to members that it and other business groups "have received multiple reports" that the Trump administration is prepared to notify South Korea of its intent to withdraw from KORUS on Tuesday, and possibly sooner.
The U.S. president has previously vowed to stop North Korea developing nuclear weapons and said he would unleash "fire and fury" on the regime if it threatened U.S. territory.
Moon is also pursuing a diplomatic route to contain the threat from North Korea.
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North Korea has also lashed out at newspapers and even congressman in the U.S. For instance, the regime flipped out after an op-ed in the Wall Street Journal called for regime change.
Hours before the test, North Korea's state news agency KCNA had released pictures showing Kim Jong Un inspecting a silver-coloured, hourglass-shaped warhead during a visit to the country's nuclear weapons institute, accompanied by scientists.
North Korea defends its weapons programs as necessary to counter perceived US aggression, such as recent air maneuvers with South Korean and Japanese jets.
A hydrogen bomb can achieve thousands of kilotons of explosive yield - massively more powerful than some 10 to 15 kilotons that North Korea's last nuclear test in September was estimated to have produced, similar to the bomb dropped on Hiroshima, Japan, in 1945.
North Korea further raised regional tensions on Tuesday by launching an intermediate-range ballistic missile over Japan, drawing global condemnation.
Impoverished North Korea and the rich, democratic South are technically still at war because their 1950-53 conflict ended in a truce, not a peace treaty.
The South Korean government, based on its alliance with the United States, is fully prepared to make responses to any North Korean threats and would not budge an inch at all in protecting the people's lives and national security.