Medvedev and Lee held their first meeting since becoming presidents of their respective countries on the last day of the G8 summit in Hokkaido.
"We will look forward to seeing you in late September," the Russian president said.
Medvedev praised "reasonably good" bilateral cooperation in all spheres and said a number of significant economic projects could be discussed during Lee's visit to Russia.
Economic analysts expect trade between Russia and South Korea to reach $20 billion this year. The two countries posted $15 billion in trade in 2007.
Speaking about the denuclearization of the Korean peninsula, Medvedev assured Lee that Russia would continue its efforts as a mediator.
Under an international energy assistance program, Russia has supplied 100,000 metric tons of heating oil to North Korea in exchange for a pledge to abandon its nuclear program. Russia plans to deliver another 100,000 metric of fuel to the North by October.
The six-party negotiations over the North's nuclear program, which include Russia, the United States, China, Japan and the two Koreas, stalled late last year when Pyongyang missed a deadline to hand over nuclear data as part of a deal under which the North was promised economic aid and diplomatic incentives.
However, the talks were given new life when North Korea handed over detailed data on its nuclear activities in late June. It also demolished on June 27 the cooling tower at its main Yongbyon nuclear complex, about 100 km (62 miles) north of Pyongyang.
Talks with North Korea on its nuclear program are set to restart Thursday in Beijing.
