The Society of Erekle II, named after the Georgian king who requested Russian protection in 1783, says the association's goal could be achieved through developing cultural ties and dialogue between the people.
"We believe that when a situation as difficult as that where a country loses territory and people die and two neighbors and nations sharing the same religion speak to each other using the language of arms - it's not normal and shameful and a sorrow for both nations," said the society chairman, Archil Chkoidze.
Tbilisi severed relations with Russia, which recognized South Ossetia and Abkhazia after a brief war with Georgia following an attack on South Ossetia by Georgian troops in a bid to regain central control over the former breakaway region in early August.
Chkoidze said the idea of setting up the association to bring a thaw to the already frozen relations arose before the August war but the "military conflict between Georgia and Russia somehow got in the way of this idea."
"But after a serious rethink we came to the conclusion that the existence of such a society today is as topical as it was before the war," Chkoidze said.
He said the name of the new organization has a "special meaning" as the actions of the Georgian king have been widely criticized. However, he said this was the "only right decision that saved the Georgian people from physical destruction and preserved the Orthodox Church."
Relations between Russia and Georgia have soured ever since pro-Western president Mikheil Saakashvili came to power in the former Soviet republic on the back of the so called rose revolution in 2003.
Georgia's new West-oriented policy, Russia's presence in Georgian conflict zones, and a ban by Russia on Georgia's key imports, mineral water and wine, have marred relations even further.