"We are not going to unite with anyone," Sergei Bagapsh told a French TV channel, France-24, in an interview Wednesday.
Russia has recognized Abkhazia and South Ossetia as independent countries, but most other governments maintain that they are still part of Georgia.
Also Wednesday, Russia sent warships into Abkhazian waters.
"The vessels' task is to prevent transportation of arms. We're also performing a humanitarian mission," Vice-Admiral Sergei Menyailo, commander of the Novorossiisk naval base, said.
Abkhazia, with a population of less than 200,000, lies on the Black Sea and has a longer border with Russia than it does with Georgia. South Ossetia, which has about 70,000 people, is a Russian-speaking enclave along the border between Georgia and Russia.