Russia's State Duma is debating whether to consider the joint bid, which comes in the wake of Kosovo's independence declaration from Serbia -- a move that many in the West encouraged but Moscow staunchly opposed.
Duma deputies planned to hear appeals by parliamentary deputies from all three separatist, former Soviet provinces as part of their bid to gain independence.
Russia's lower house of parliament is expected to adopt a resolution on the Abkhaz, South Ossetian, and Transdnistrian regions' status.
Abkhazia and South Ossetia, which broke away from Georgia in conflicts in the early 1990s, and Transdniester have each urged the international community to recognize their sovereignty.
Their call came on the heels of the Kosovar declaration on February 19, which has since been recognized by dozens of other countries.
The self-declared presidents of the three regions -- Abkhazia's Sergei Bagapsh, South Ossetia's Eduard Kokoity, and Transdniester's Igor Smirnov -- met in Moscow on March 12 to discuss their joint independence bid.
Officials from Russia's Foreign, Defense, and Economic Development and Trade ministries were expected to attend the Duma debate.
Despite strongly backing the three regions, Moscow has yet to recognize their self-declared governments.
A number of Russian politicians, like State Duma deputy speaker Sergei Baburin, nonetheless openly support the provinces' independence drive.
"Abkhazia, South Ossetia, and Transdniester have been recognized," Baburin said. "As a lawyer, I can tell you that there are international documents signed by the presidents of these republics, by the presidents of Georgia, Ukraine, and Moldova, by OSCE representatives, as signatories enjoying equal rights. And this means recognition."
A formal acknowledgement of independence would be sure to raise fury in Moldova and Georgia, whose ties with Moscow have soured in recent years.
Dozens of Georgians were gathered outside the Russian Embassy in Tbilisi to protest the debate as the Duma convened.
Georgian Foreign Minister David Bakradze has urged Russia not to launch the process of recognition, let alone recognize, the independence of Abkhazia and South Ossetia at the Duma session.
"We count on the good sense of Russian deputies to prevail," he said.
Russia has warned the West that the recognition of Kosovo's independence will embolden separatist movements around the world, including on former Soviet territory.
Russia's new ambassador to NATO, Dmitry Rogozin, also said this week that Abkhazia and South Ossetia will secede if NATO takes steps toward granting Georgia NATO membership.
But political analysts say Moscow has stopped short of recognizing Abkhazia, South Ossetia, and Transdniester for fear this will boost the Chechen separatist movement on its own territory.
Mikhail Aleksandrov, a Caucasus expert at Russia's CIS Institute, said it was too early for Moscow to grant formal recognition to Georgia and Moldova's breakaway regions.
"Personally, I don't think that things now will go as far as a formal recognition of Abkhazia and South Ossetia," Aleksandrov said. "It would be illogical for us, after opposing the Kosovo precedent, to immediately recognize Abkhazia, South Ossetia, and Transdniester. It would go against logic and undermine our whole diplomatic position on the international scene."
Moscow's stance appears to be contributing to impatience in the breakaway provinces.
In comments published by the Russian daily "Kommersant" on March 13, Transdniester's Smirnov lambasted Russia for lacking the "courage" to help the three regions achieve independence.
RFE/RL's Russian Service contributed to this report