Dmitry Medvedev and Yasuo Fukuda met on the sidelines of the G8 summit currently underway in Hokkaido.
"No substantial progress has been made on finding a mutually acceptable way out, but we are getting closer to understanding each other's positions," Sergei Prikhodko said, adding that Russia wanted a patient and peaceful dialogue with Japan over the issue of the South Kuril Islands.
According to Prikhodko, Fukuda said Japan was willing to receive Russian Foreign Minister Sergei Lavrov on a visit within the next few months.
The Japanese leader also invited Medvedev to pay an official visit to Japan.
"In his turn, Medvedev expects Fukuda to be his guest at an appropriate time," the Kremlin aide said.
Medvedev and Fukuda also agreed to meet at an APEC summit in Peru in November.
A high-ranking diplomatic source said on Monday Japan expected the Russian president's visit to the G8 summit to give an impetus to the long-standing territorial dispute.
However, Medvedev said it was impossible "to achieve maximum results over a short period of time."
Russian Foreign Ministry spokesman Andrei Nesterenko said last week Russian sovereignty over the South Kurils was unquestionable.
The lower part of the chain of Pacific islands stretching from the Kamchatka Peninsula on the Russian mainland to the northeast coast of Japan's Hokkaido island was annexed by the Soviet Union after World War II and the dispute has prevented the two countries from signing a formal peace agreement.