North Korean leader Kim Jong Un looks up at the sky at what is said to have been a missile launch in this image taken from a news bulletin aired by state-run broadcaster KRT on Wednesday.
North Korea and its recent provocations will likely top the agenda at the one-on-one meeting, as it follows the communist state's testing of its sixth and possibly most powerful nuclear bomb.
He said diplomacy was the only answer.
Russia is seen to have some influence over North Korea: While China accounts for nearly 90 per cent of trade with North Korea, Russia is the North's second- largest trade partner, with bilateral trade reaching US$84 million (S$114 million) in 2015, according to South Korean statistics.
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.
When asked to comment on the U.S. probe into alleged ties between Trump's campaign team and Russian intelligence, Putin said, "It's America's internal political issue and not Russia's business".
"They'll eat grass, but they won't abandon their program unless they feel secure", Russian state news agency TASS reported the Russian President as having said.
NATO urged all countries to step up efforts to enforce sanctions on North Korea and stop its weapons tests - an appeal that diplomats said was aimed at the reclusive state's trading partners, suspected of holding back on penalties. If they are removed from the equation, Putin said, Russian Federation has fewer than 455 diplomats in the United States.
"It is not worth giving in to emotions and driving North Korea into a corner".
It is estimated that over 50,000 North Koreans are now working overseas with much of their pay going to the Kim Jong-un regime.
"I don't think it was wise for the president to extemporaneously threaten nuclear war with North Korea".
British Defence Secretary Michael Fallon said on Wednesday China held the key to resolving the crisis, reiterating comments made by Prime Minister Theresa May and Australian leader Malcolm Turnbull after they spoke with Trump.
"We too are opposing and denouncing North Korea's nuclear development".
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Such measures should include completely cutting off the oil supply to the impoverished North, Moon has said. Putin said the United States had a right to close consulates but "it was done in such a rude way".