Mr Moon, the son of North Korean refugees, has continued to seek dialogue even as he bolsters South Korea's defences.
He has also called on his generals to draw up a detailed timetable to complete a last-resort strategy to strike North Korean nuclear sites, intercept missiles and take out its leadership.
Russian President Vladimir Putin has called for talks with North Korea, saying sanctions are not a solution. It's a US commitment that has guided the actions of American friends and foes alike.
He first expressed his contempt for U.S. elites as "people who confuse Austria with Australia".
Pressed on whether he could accept a scenario in which the isolated nation had nukes but was "contained and deterred", Trump demurred.
"I personally think if this had to be implemented it would have to be temporary, done to a limited degree, or run as a trial", said Lu Chao, a North Korea expert at China's Liaoning Provincial Institute of Social Science.
"South Korea may face the most complex strategic environment in Asia", write Sung Chull Kim and Michael D. Cohen, editors of a new collection of scholarly essays titled "North Korea and Nuclear Weapons: Entering the New Era of Deterrence".
Speaking to The Associated Press on Tuesday, former South Korean Foreign Minister Yoon Young-kwan acknowledged that North Korea's more powerful bombs and further-reaching missiles are sparking debate about his country's long-term security strategy.
Meanwhile, Sweden urged its citizens Friday to refrain from unnecessary trips to North Korea.
On Sunday, North Korea tested a nuclear device that had a yield estimated at ten times that of the atom bomb dropped by the United States on Hiroshima in 1945. The liberal Moon took office in May calling for diplomacy with Pyongyang but the escalation in weapons tests has been the North's only response. The Vienna Convention on Consular Relations provides that consular posts are established only with the host state's consent.
"For Russia and China, the North Korea nuclear program is an indirect threat".
During the BRICS news conference, Putin also addressed the situation with North Korea.
But the nuclear test changed all that. His military has maintained a torrid pace in testing weapons, which also include solid-fuel missiles built to be fired from road mobile launchers or submarines. Japan, the United States and South Korea should step up their cooperation in urging Russian Federation and China to intensify their pressure on North Korea to force the country to abandon its provocative acts.
Washington, Seoul and Tokyo have been pushing for stronger sanctions to punish Pyongyang over its nuclear activities, such as denying the country oil supplies.
Inviting U.S. nuclear weapons would be an attempt by Japan jolt China, North Korea's sole major ally, to do more to rein in its neighbour by showing there are consequences to North Korean provocations that threaten its neighbours and destabilize the region, the policy maker said.