Mr Moon, a liberal who took office in May, had initially showed a preference for a diplomatic approach on North Korea, but his government has since taken a harder stance as the North continued its pace in weapons tests.
Dozens have been injured in clashes between protesters and police in a South Korea farming village where the USA military will begin installing additional launchers to a contentious US missile defense system. Moreover, Seoul said that no military response to the North Korean crisis is acceptable.
South Korea is also working on a 'decapitation strike' team that would be deployed to eliminate the North's leadership if war broke out.
Meanwhile, Japanese Defense Minister Itsunori Onodera said the explosive device detonated deep under a North Korean mountain Sunday had a yield of up to 160 kilotons.
Mr. Putin denounced North Korea's sixth and largest nuclear bomb test on Sunday, saying Russian Federation did not recognise its nuclear status.
"This leads nowhere", Putin said, speaking alongside South Korean President Moon Jae-in, Japanese Prime Minister Shinzo Abe and Mongolian President Khaltmaa Battulga at the Eastern Economic Forum in the far eastern Russian city of Vladivostok. In a diplomatic victory for the Trump administration, the United Nations last month approved sweeping new sanctions targeting roughly one-third of the North's economy, with China's support.More news: Five takeaways from Houston's Week 1 loss to Jacksonville
"Especially regarding the new East policy you are pursuing and the new defense policy I am pursuing, it makes me feel that we are dreaming the same dream", said Moon.
North Korea said it tested an advanced hydrogen bomb for a long-range missile on Sunday, prompting global condemnation and a USA warning of a "massive" military response if it or its allies were threatened.
Seoul has routinely dismissed the option of basing USA nuclear weapons on South Korean soil for the first time since the 1990s, but the country's defence minister, Song Young-moo, said "all available military options" were being considered to address the growing threat from North Korean missiles.
The Security Council has imposed seven sets of sanctions on North Korea since it first tested a nuclear device in 2006, though Pyongyang has repeatedly found ways to circumvent the measures.
After the meeting, Abe and Moon issued a statement saying "now is the time to further increase sanctions and pressures against the North as much as possible rather than seeking dialogue", according to Moon's spokesman Yoon Young-chan. The two leaders spoke for approximately 40 minutes by phone.
The announcement dramatically upped the stakes in its standoff with the worldwide community over its banned weapons programmes, which have seen it subjected to seven sets of UN Security Council sanctions so far. Putin did not say how close the two countries were to such an agreement.
"The recent self-defense measures by my country, DPRK, are a gift package addressed to none other than the U.S.", Han told a disarmament conference, using the acronym for North Korea's formal name, the Democratic People's Republic of Korea.