The flight was scheduled for 08:30 local time (22:30 GMT on Saturday), but was delayed due to heavy fog.
"The situation has not changed and it was decided to postpone the flight for tomorrow, setting it for the same hour as was originally scheduled for today," one of the organizers said reporters.
On Saturday, Japan's Nakashibetsu settlement on the Hokkaido island hosted a ceremony devoted to the first flight between Japan and Southern Kuril Islands, which is expected transfer 70 islands’ former residents who wish to visit ancestral graves there.
Japan's State Minister for Foreign Affairs Nobuo Kishi said during the ceremony that the launch of the flight was a "big step" toward improvement of conditions for the Japanese to visit the islands, which Tokyo calls the Northern Territories.
A plane of Russia's Far East air carrier Aurora is set to leave Hokkaido for Kunashir. The flight program also includes visiting the Iturup island.
On April 27-28, Japanese Prime Minister Shinzo Abe visited Russia and held talks with Russian President Vladimir Putin, during which the sides reached an agreement to provide an opportunity for former Kuril Islands' residents to travel to the islands by plane without visas.