He also added that South was ready for any attempt of strike from North and was capable of striking back should Pyongyang attack.
"Every test he makes ... takes North Korea one step closer to being able to deliver a nuclear-tipped missile anywhere in the world".
North Korea, which has defied calls to rein in its weapons program - even from its lone major ally China, has been working on a missile mounted with a nuclear warhead capable of striking the USA mainland.
Any peace overtures will likely be dampened by the worldwide community's response to Sunday's test by the North of the country's new Hwasong-12 ballistic missile.
Moon briefly stopped by the meeting to greet Pottinger, Yoon said. However, the Korean Central News Agency, which is controlled by Pyongyang, said that the Hwasong-12, as the missile fired on Sunday is being called, is "capable of carrying a large-size heavy nuclear warhead". Pyongyang is threatening a sixth nuclear test.
After Sunday's launch, Pyongyang gleefully hailed significant advances in developing a nuclear missile capable of reaching the U.S. mainland.
Defense experts say that North Korea's Taepodong missile resembles Iran's Shahab missile.
Also Tuesday, Adm. Harry Harris Jr., the top American military officer in the Pacific, met with Japanese Prime Minister Shinzo Abe in Tokyo to discuss the North Korean missile launch.
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US Ambassador Nikki Haley accused North Korea of intimidating the entire global community with its nuclear programme, military ability and cyberattacks.
The U.S. ambassador said Russian Federation has the same decision to make as the rest of the worldwide community: "You either support North Korea or you don't, but you have to choose". "We believe South Korea will bring clear measures to improve relations".
'The risky behaviour by North Korea is not just a threat to the Korean peninsula.it's a threat to China, it's a threat to Russia, ' Harris told a an academic forum in Tokyo.
A separate summit could also be held the following month, Lee said.
But critics of the deal in South Korea said Japan did not go far enough, and earlier this year Tokyo recalled its ambassador over a statue symbolizing "comfort women", which was erected outside its consulate in the South Korean city of Busan.
South Korea's Yonhap News notes that Moon has promised to increase South Korea's defense budget from the current 2.4 percent of GDP to 3 percent.
South Korean Unification Ministry spokesman Lee Duk-haeng told reporters the government's most basic stance is that communication lines between South and North Korea should reopen.
He said in order to put pressure on North Korea, sanctions must be implemented by countries working together in bilateral relationships. If accurate, it would be the highest of any of North Korea's recent missile launches.