"So I wish to work together to have North Korea stop its provocations and find ways to fundamentally resolve the North Korean nuclear issue", Moon added.
"It's counterproductive to inflate this military hysteria".
Moon earlier met with Putin and urged Moscow to support stronger sanctions, but Putin called for talks with North Korea, saying sanctions are not a solution.
Putin, while condemning North Korea's missile and nuclear development as posing a threat to worldwide and regional peace and safety, said, "There are only political and diplomatic means to resolve the nuclear problem on the Korean Peninsula".
North Korea's Minister of External Economic Relations Kim Yong Jae, who is at the forum, said his country will "respond to barbaric attempts to exert pressure by the USA by our strong countermeasures", according to the Russian state-run Tass news agency.
Moon said his nation was increasing pressure on Pyongyang in the hope of achieving a diplomatic and peaceful resolution to the crisis. But after North Korea conducted its second flight test of a developmental intercontinental ballistic missile in July, Moon ordered his military to work with USA commanders in South Korea to temporarily place more launchers before the reviews are conducted.
China and Russian Federation, which also have denounced the nuclear test, are calling for more dialogue.
North Korea drew wide condemnation after it hailed on Sunday the successful testing of a missile-ready hydrogen bomb, which created a blast said to be more destructive than the atomic bombs dropped on Japan in World War II. "They count on a specific reaction from the partners and they get it".
Japanese Prime Minister Shinzo Abe said on Wednesday that he wants North Korea to understand it has "no bright future" if it continues on its current path and that the reclusive country needs to change its policies.
"Japan and Russian Federation will work together in the global society for that", Abe said in televised statement. "We estimate this was far bigger than previous nuclear tests".
Diplomats have said the Security Council could consider banning North Korean textile exports, barring its airline and stopping supplies of oil to the government and military.
"The time for half measures in the Security Council is over".
"We can not resolve this situation without diplomatic tools, without talks". The U.S. has said it wants the council to take up tougher sanctions at a meeting September 11.
Haley may have trouble getting other Security Council members - especially Russian Federation and China, who each hold veto power - to sign onto the draft sanctions as they're now written.
Putin and Moon met on the sidelines of an economic summit in the far eastern Russian city of Vladivostok amid mounting global concerns that their shared neighbor plans more weapons tests, possibly a long-range missile launch ahead of a key weekend anniversary.
Abe will meet Putin on Thursday.
But Putin praised the recent expansion in Japan-Russia trade and business ties.
The leaders' comments came hours after South Korea bolstered its defenses against North Korean rockets, with the arrival of four launchers for a US missile shield at a military base in South Korea.
"The situation is very grave".
Prime Minister Lee Nak-yon said at a conference in Seoul on Thursday that North Korea may fire its next missile on Saturday - the anniversary of its founding - adding there isn't much time until the regime becomes a fully nuclear-armed state.
With its relations with China still sour over its deployment of a USA missile shield, South Korea is looking to Russian Federation for support.
Russian Federation and China opposed the deployment of the Terminal High Altitude Area Defense (THAAD) system, as both say it has the potential of fueling an arms race.