Japanese Foreign Minister Taro Kono is planning to meet his Russian counterpart, Sergei Lavrov, next week.
The meeting may take place on the sidelines of the United Nations General Assembly in New York.
Russian President Vladimir Putin earlier this month suggested that the countries sign a peace treaty without any conditions by the end of the year.
In response, Abe conveyed Japan's stance that the country will conclude a peace pact after the issue of the Northern Territories is resolved.
Russia controls the 4 islands. Japan claims them.
The Japanese government maintains the islands are an inherent part of Japan's territory. It says the islands were illegally occupied after World War Two.
At the expected talks with Lavrov, Kono will seek to determine what lay behind Putin's remarks regarding the islands.
Kono also wants to confirm that the 2 countries will speed up arrangements for joint economic activity on the 4 islands.
Abe and Putin have endorsed a plan on the activity.
Kono also hopes his meeting with Lavrov will help Abe and Putin reach an agreement at a summit in the near future.