A day earlier, he had said "all options are on the table" following North Korea's Tuesday launch of a missile over Japan.
"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.
That launch came after Pyongyang tested two intercontinental missiles in July and claimed to have the United States mainland within its range.
Despite Pyongyang's snub of Moon's invitations for talks in July, the South Korean president continued to emphasize the importance of dialogue with its neighbor in the phone call with his American counterpart.
Chung also said President Moon plans to hold talks over the phone with U.S. President Donald Trump at an early date to discuss the situation.
The South Korean president insisted the North's latest nuclear test was a clear mistake that will only accelerate its isolation.
It also objected to the translated title of the South Korean edition as "Capitalist People's Republic of Korea" and the book's cover that replaced the red star in North Korea's official seal with the US dollar mark.
Investigation into attack on Kh Izhar-ul-Hassan underway: IG Sindh
The Sindh police chief said after the MQM had split, the leaders of Pakistan faction had been warned of the dangers it might face. The martyred constable, Moin, was on guard duty with the Leader of the Opposition in Sindh Assembly, Khawaja Izhar-ul-Hassan.
However, Trump said after the latest missile test that negotiations with Pyongyang were "not the answer".
China, North Korea's sole major ally, said it strongly condemned the nuclear test.
That followed the test launch of two long-range ballistic missiles in July in a sharply lofted trajectory that demonstrated a potential range of 10,000 km (6,000 miles) or more that would put many parts of the US mainland within striking distance.
"The power is 10 or 20 times or even more than previous ones", said Kune Y. Suh, a nuclear engineering professor at Seoul National University.
"North Korea's mission is quite clear when it comes to this latest atomic test: to develop a nuclear arsenal that can strike all of Asia and the USA homeland", Harry Kazianis, director of defence studies at the conservative Center for the National Interest in Washington, said.
Earthquakes triggered by North Korean nuclear tests have gradually increased in magnitude since Pyongyang's first test in 2006, indicating the isolated country is steadily improving the destructive power of its nuclear technology. Kim Hyun-bin, Arirang News. It says its weapons programmes are needed to counter USA aggression. The two countries technically remain at war since a truce agreed to end the 1950-1953 Korean War was never followed by a peace agreement.
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.