The statement came amid a dispute between the unrecognized republic, Russia and Georgia over the alleged downing of Georgian drones over Abkhazia, and with Moscow and Tbilisi trading accusations of military expansion in the territory.
"We are proposing the broadest possible military presence to Russia," Sergei Shamba said in an interview published in the respected Russian daily Izvestia on Tuesday.
"We agree that Russia should bring our territory under its military control, but in return demand security guarantees," he said.
The unrecognized republic claimed on Sunday it had downed two Georgian drones over its airspace and said on Monday it had detected two more unmanned reconnaissance planes, but had taken no action. Georgia dismissed the reports as "absurd," accusing the region of trying to escalate tensions.
The announcement came two weeks after Georgia accused Russia of shooting down an unmanned drone over Abkhazia, which Tbilisi considers its sovereign territory. Moscow has denied involvement in the incident.
Russia, which has administered a peacekeeping contingent in Georgia's breakaway regions Abkhazia and South Ossetia since bloody conflicts in the 1990s, dispatched additional troops to Abkhazia recently to deter what it calls a planned Georgian military offensive. Tbilisi accuses Russian troops of siding with separatists.
Moscow has also moved to step up ties with Georgia's breakaway republics against the backdrop of the Caucasus state's NATO bid and Western recognition of Kosovo's independence from Serbia. Russia, however, has not recognized the region.
Western nations criticized Russian moves toward Abkhazia and South Ossetia.
Shamba said greater support from Russia marked "the emergence of interstate relations" between Abkhazia and Russia. But he added that the self-proclaimed republic had no plans to join Russia so far.
Russia's foreign minister said on Tuesday Moscow was not planning to bring Abkhazia under its military control.
"No proposals have been made on this. I do not think the possibility is being discussed," Sergei Lavrov said.
Located on a key Europe-bound route for Caspian oil and natural gas route, Georgia has been at the center of a struggle for influence between the West and Russia since the collapse of the Soviet Union.
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The clash of Russian and Western interests has given rise to a geopolitical battle. German politicians are trying to leave all doors and windows open for dialogue with Russia. Moscow does acknowledge this, and Germany is probably the only country with which it is ready to discuss European security.