Fukuda will seek to enhance economic ties and for closer cooperation at the July Group of Eight summit, Kyodo news service reported.
The dispute over the four Russian-administered islands is also likely to come up in his talks, the report said, adding the emphasis, however, would be on developing mutual trust among the leaders.
"Looking at the global situation, I think it is time for us to mutually cooperate with Russia extensively on bigger issues," Fukuda said before leaving.
"We will hold discussions centering on such matters but for that I want to steadily talk about the major issue of resolving the territorial dispute and concluding a peace treaty and hope that we can make even one step forward."
While Russia is seen as being keen for Japanese participation in developing East Siberia and improving energy efficiency, Japan would like more energy supplies from Russia to lessen dependence on Middle East sources.