Putin and Moon met on the sidelines of an economic forum in Vladivostok on Russia's Pacific coast.
Speaking after the talks, the two men said that resolving the North Korea crisis as soon as possible was their top priority but they appeared to have diverging views on the problem.
"In order to compel North Korea to come to the dialogue table, UN sanctions must be strengthened. Now it is inevitable to cut off oil supplies to the North, we hope Russia will cooperate as well," Moon was quoted as telling Putin by presidential spokesman Yoon Young-Chan, Yonhap news agency reported.
The South Korean presidential spokesman quoted Putin as saying that Russia was concerned that the blockage of oil supplies would hurt civilians including hospitals.
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Putin said Russia exported a negligible amount of oil to North Korea - about 40,000 tonnes a year, according to Yoon.
Putin's spokesman Dmitry Peskov was not immediately available for comment.
Putin stressed the need for a political solution, saying further sanctions and pressure would not solve the problem.
"Today, as never before, everyone needs to show composure and avoid steps that lead to an escalation of tensions," he said.
"It is not worth giving in to emotions and driving North Korea into a corner."
Moon said after the talks: "It is more important than anything else to resolve the North's nuclear and missile issues, which are the most urgent and gravest challenges facing this region, at an earliest date."
"I and President Putin also agreed that the missile development pursued by North Korea is a wrong path and it is an urgent task to ease tension on the Korean peninsula," he told reporters.
Russia has rebuffed US calls for new UN sanctions while Washington has promised its allies advanced weaponry.
Yesterday, Putin warned of a global catastrophe unless a diplomatic solution was reached over North Korea, rejecting US calls for more sanctions as "useless", widening the split between major powers over how to rein in Pyongyang.