Lee will go on to France for a Group of 20 summit in Cannes on Thursday and Friday, the presidential Blue House said.
The two leaders, at a meeting in Saint Petersburg Wednesday, "will exchange ideas on issues concerning the Korean peninsula, including the North Korean nuclear problem, and the Northeast Asian region", it said.
Diplomatic efforts have resumed to revive six-party talks on the North's nuclear disarmament, which group the two Koreas, China, Russia, the United States and Japan.
Pyongyang formally quit the six-party forum in April 2009, a month before staging its second atomic weapons test.
It has since repeatedly said it wants to come back without preconditions but Washington and its allies say it must demonstrate its commitment to denuclearisation by deed, not words.
A Seoul presidential official said the leaders are also likely to discuss a longstanding idea to transport Russian natural gas to South Korea via the North.
The project returned to the headlines after it received the blessing of the North's leader Kim Jong-Il during his summit with Medvedev in August.
But a presidential official told Yonhap new agency that discussions between Seoul and Moscow could make meaningful progress only after Russia and the North agree on pipeline transit fees.
Lee, who chaired last year's summit in Seoul of the G20 advanced and developing countries, will then attend the Cannes event.
Its agenda includes ways to tackle the eurozone debt crisis, macroeconomic policy coordination, reform of the international currency system, financial safety nets and other issues facing the global economy.