Prime Minister Lee thanked President Putin for Russia's support towards establishing permanent peace and denuclearization on the Korean Peninsula, and said that the South Korean government was doing its best to implement what was agreed in June, between Presidents Moon Jae-in and Putin, including the "nine bridges" of cooperation between South Korea and Russian Federation.
On Monday, after the pair met on the sidelines of the annual event, Putin said it "would be naive" to think the territorial dispute over Russian-controlled islands to Japan's north could be solved quickly.
In a move that took Japanese officials by surprise, Putin publically proposed to Abe that the two sign peace treaty to end World War II.
But a Japanese government spokesman said Japan's position had not changed and that the issue of sovereignty over the islands needed to be resolved before signing any treaties with Russian Federation.
Putin was also late for a December 2016 summit in Japan, arriving three hours later than scheduled.
After numerous meetings over the past few years between Abe and Putin, they have launched various economic projects on the islands in areas such as the farming of fish and shellfish, wind-generated energy, and tourism. "We are both fully aware that it will not be easy". "Let's conclude a peace treaty before the end of this year, without any preconditions".
Russian Federation and Japan are in dispute over a chain of Pacific islands and as a result have still not formally ended their World War Two hostilities. Abe did not give a response. In 1956, Japan and the Soviet Union agreed to end "the state of war" and restore diplomatic relations.
Over the years, negotiations to reach a peace agreement have seen both friendly gestures and hardline statements.
Relations between China and Japan soured in 2012 over a territorial dispute over several tiny islands in the East China Sea.
The Russian leader said he wanted to clinch the peace treaty first and then continue to discuss the territorial issue with Abe as "friends", during a question and answer session of the forum's plenary meeting. "We have been negotiating for 70 years", Putin said.
Yoshihide Suga, Japan's chief cabinet secretary and top government spokesman, told a regular press briefing this week: "Our position that the Northern Territories issue is resolved before any peace treaty remains unchanged".
Upon returning to power in 2012, Abe took a firm position on Japan's claims to the disputed island chain, aggravating tensions with Beijing.