Putin and Moon met on the sidelines of an economic summit in the far eastern Russian city of Vladivostok amid mounting international concerns that their shared neighbour plans more weapons tests, possibly a long-range missile launch ahead of a key weekend anniversary.
Moon, who came to power earlier this year advocating a policy of pursuing engagement with Pyongyang, has come under increasing pressure to take a harder line on North Korea.
He said on Tuesday the United Nations should consider tough new sanctions on North Korea, including halting oil shipments, after Sunday's nuclear test.
However, Russia has reacted coolly to the prospect of more sanctions, with Putin saying on Tuesday it was a "road to nowhere".
Sanctions have so far done little to stop North Korea boosting its nuclear and missile capacity as it faces off with U.S. President Donald Trump, who has vowed to stop Pyongyang from being able to hit the U.S. mainland with a nuclear weapon.
U.S. Ambassador to the United Nations Nikki Haley accused North Korean leader Kim Jong Un on Monday of "begging for war" with a series of nuclear bomb and missile tests. She urged the 15-member Security Council to impose the "strongest possible" sanctions to deter him and shut down his trading partners.
Japanese Prime Minister Shinzo Abe, who will discuss North Korea with Moon and Putin in Vladivostok, said on Wednesday he wanted the North to understand it has "no bright future" if it continues on its current path.
"More gift packages"
A top North Korean diplomat warned on Tuesday his country is ready to send "more gift packages" to the United States. South Korea's Unification Ministry said on Wednesday it was still expecting more activity from the North.
Han Tae Song, Pyongyang's ambassador to the United Nations in Geneva, confirmed that North Korea had successfully conducted its sixth and largest nuclear bomb test on Sunday.
"The recent self-defence 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.
"The U.S. will receive more 'gift packages' ... as long as it relies on reckless provocations and futile attempts to put pressure on the DPRK," he said without elaborating.
Asian stocks tracked Wall Street's slide overnight to slip on Wednesday, while the dollar was on the defensive with tensions in the Korean peninsula showing few signs of abating.
Japan upgraded its assessment of the North Korean test to 160 kilotons from 120 kilotons after the size of the earthquake it generated was revised to 6.1.
"Calculating based on this number, the estimated yield was 160 kilotons," Defence Minister Itsunori Onodera told reporters. "We estimate this was far bigger than previous nuclear tests."
Satellite imagery appeared to show the blast caused numerous landslides at North Korea's Punggye-ri test site, according to 38 North, a Washington-based North Korean monitoring project.
South Korean officials said they continued to monitor for radioactive fallout from the test and for signs of preparations for more activity as they pushed for a stronger international response.
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.
Other measures could include preventing North Koreans from working abroad and adding top officials to a blacklist aimed at imposing asset freezes and travel bans.
Trump and British Prime Minister Theresa May agreed in a telephone call on Tuesday that China, the North's main ally and trading partner, must do more to persuade North Korea to cease its missile tests, a spokesman for May said.
Australian Prime Minister Malcolm Turnbull also spoke with Trump and reiterated calls for China to use its leverage to bring North Korea in line.
China and Russia have advocated a "freeze for freeze" plan, where the United States and Seoul halt major military drills in exchange for North Korea halting its weapons programmes, but neither side is willing to budge.
North Korea says it needs to develop its weapons to defend itself against what it sees as U.S. aggression.
South Korea and the United States are technically still at war with North Korea after the 1950-53 Korean conflict ended with a truce, not a peace treaty.
( By Denis Pinchuk and Christine Kim. Additional reporting by Stephanie Nebehay in GENEVA, Christian Shepherd in BEIJING, Michelle Nichols at the UNITED NATIONS, and Tim Ahmann and David Shepardson in WASHINGTON; Writing by Lincoln Feast; Editing by Paul Tait)