Meeting on the sidelines of a business forum on Russia's Pacific coast, the two leaders agreed that officials on both sides would keep working on a draft deal that Abe and Putin would consider when the Russian leader visits Japan in December.
Though Russia and Japan have strong diplomatic and commercial ties, the dispute has prevented them signing a treaty formally ending their World War Two hostilities.
"Particularly regarding a peace treaty, the two of us alone had quite an in-depth discussion. It is now clearer how to proceed in talks based on the 'new approach'," Abe told reporters.
"Finding a solution through leaders' mutual trust would be the only way to break away from this abnormal condition, where no peace treaty has been concluded for more than 70 years."
Abe said he wanted the December summit with Putin to take place in his home town of Nagato city "in a relaxing atmosphere so that talks on a peace treaty would accelerate."