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.
The two leaders pledged to continue applying strong diplomatic and economic pressure on the regime and take necessary preparations to deter and defend against North Korea's growing threats.
Moon and U.S. President Donald Trump spoke by telephone Friday, officials in Washington and Seoul said.
Tensions on the Korean peninsula have been high since last month when North Korea threatened to launch missiles into the sea near the strategically located US Pacific territory of Guam after Trump said Pyongyang would face "fire and fury" if it threatened the United States. -South Korean free trade deal with his advisers next week, in a move that could see him pull out of the accord with a key American ally at a time of heightened tensions on the Korean peninsula.
It came as US and South Korean forces were nearing the end of the 10-day annual Ulchi Freedom Guardian joint exercises, which the North regards as a rehearsal for invasion.
"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.
White House press secretary Sarah Huckabee Sanders denied there was any inconsistency in Trump's remarks.
Trump also gave "conceptual" approval to the purchase by the South of billions of dollars of USA military hardware, the White House said.
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The White House did not mention the voluntary bilateral agreement but said the two leaders agreed to strengthen their defense cooperation and South Korea's defense capabilities.
South Korea is now allowed to possess ballistic missiles with a range of 800 kilometers and payload of 500 kilograms, but it wants to raise the weight limit to 1,000 kilograms.
The South wants the maximum warhead weight doubled to one ton, and the Pentagon has said it was "actively" considering the revision.
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.
Trump, who has warned that the USA military is "locked and loaded" in case of further North Korean provocation, reacted angrily to the latest missile test, declaring on Twitter that "talking is not the answer" to resolving the crisis.
The South, which hosts 28,500 US troops to defend it, is banned from building its own nuclear weapons under a 1974 atomic energy deal it signed with Washington, which instead offers a "nuclear umbrella" against potential attacks.
China, North Korea's sole major ally, said it strongly condemned the nuclear test and urged Pyongyang to stop its "wrong" actions.