"The threat of clandestine Georgian actions prompts both Russia and Abkhazia to speed up talks on the issue," Sergei Bagapsh said in a statement.
The Abkhazian president also said his country was ready to "formalize cooperation with the [Russian] Black Sea Fleet."
Russia and Abkhazia have agreed to establish a Russian Black Sea Fleet base at Ochamchira, a seaside town in the separatist Georgian republic recognized by Russia as independent. No official documents have been signed, however.
Russia's Black Sea Fleet currently uses a range of naval facilities in Ukraine's Crimea as part of a 1997 agreement, under which Ukraine agreed to lease the bases to Russia until 2017.
Ukrainian President Viktor Yushchenko announced last summer that Ukraine would not extend the lease of the base in the Crimean city of Sevastopol beyond 2017, and urged the Russia to start preparations for a withdrawal.
Russian media previously reported that Russia was also looking at possible naval facilities in Yemen, Syria and Libya, among other countries. Russian military officials are also on record as saying Moscow could build up its presence in the Mediterranean to make up for the loss of Sevastopol.