Speaking to Russia's Interfax news agency, an FSB source said: "An agent has been exposed, a Russian citizen, a native of Georgia. [This] confirms the involvement of Georgian secret services in disruptive terrorist activity in the North Caucasus."
The claim comes as tensions between Georgia and Russia have dramatically escalated, centering on Abkhazia, the Russian-backed separatist region of Georgia.
The Interfax source said the suspect's work was "to organise contacts between Georgian secret services and active members of illegal armed groups on Russian territory" in order to provide financing and "organise armed resistance".
The source said: "For fulfiling his tasks the agent several times received financial rewards from Georgia's special services in American dollars. Some of these were handed over in personal meetings, some by... money transfer."
Shota Utiashvili, a Georgian interior ministry spokesman, said: "It is an absurd accusation. Russia's provocations are becoming more and more aggressive."
|Georgians protest against Russia's support|
of Abkhazia [AFP]
Tensions between Russia and Mikheil Saakashvili, Georgia's president, have risen as Georgia pursues membership of the Nato military alliance.
Georgia received a promise of eventual Nato membership, at an unspecified date, at a summit of Nato leaders in Bucharest last month.
Saakashvili has also sought to retake control of Abkhazia and South Ossetia, a second separatist region, which are both backed by Russia.
Tbilisi and Moscow have traded spying accusations before, notably in September 2006, when Georgia arrested four alleged Russian spies.
Amid Georgian hopes of an easing of tensions under Dmitry Medvedev, Russia's new president, a Georgian interior ministry official said his country was "astonished that the new head of the FSB has begun his first day with the discovery of so-called Georgian spies".
Last month, Russia announced it was establishing formal ties with Georgia's two separatist regions, even though it claims to recognise Georgia's territorial integrity.
In an example of the growing ties, a Russian Olympic official and the governor of the neighbouring Russian region of Kuban held talks in Abkhazia on Friday on building plans for the 2014 Winter Olympics in Russia, the Interfax news agency said.
Moscow has increased its peacekeeping force in Abkhazia, a force long seen as giving de facto backing to the Abkhazians.
In recent weeks, Abkhaz separatists claim to have shot down a string of Georgian reconnaissance drones.
Tbilisi has denied those claims, saying that just one drone has been destroyed by a Russian fighter jet.