Russia has traditionally dominated all three of these post-Soviet organizations.
"We will send membership applications to these structures, and we hope they will be accepted," Sergei Bagapsh said at a joint news conference with S. Ossetian leader Eduard Kokoity in Moscow.
Kokoity said that he fully supported the statement of the Abkhazian president.
"This is a logical step in the development of our states. We will strengthen these relations with time," he said.
Russia signed friendship and cooperation treaties with the rebel Georgian republics earlier on Wednesday, promising them military and economic support.
Georgia served notice of its withdrawal from the CIS, an alliance of former Soviet republics, on August 18, 2008, following a 5-day war with Russia over S. Ossetia. Its withdrawal becomes effective on August 17, 2009.
The CSTO is a security grouping comprising Armenia, Belarus, Kazakhstan, Kyrgyzstan, Russia, Uzbekistan and Tajikistan.
The Russia-Belarus Union State is a supranational entity consisting of the Russian Federation and the Republic of Belarus. It was formed in 1996 "with the intention of providing greater political, economic, and social integration."
Moscow recognized South Ossetia and Abkhazia as independent states on August 26. Most residents of both South Ossetia and Abkhazia have had Russian citizenship for several years.
Russia pledged in the friendship and cooperation treaties to help the two republics to protect their borders. The pacts also permit Russia and South Ossetia, as well as Russia and Abkhazia, to set up military bases on each other's territories.
The treaties also formalized economic cooperation between Russia and the republics, and cleared the way for dual citizenship for Russian, Abkhazian and South Ossetian nationals. Russia agreed to unify its transportation, energy, and communications infrastructure with the two republics.
South Ossetia and Abkhazia have so far only been recognized by Russia and Nicaragua. Belarus has pledged to follow suit in the near future, and Venezuela has voiced support for Russia's recognition of the two republics.
