Russia recognized the two Georgian breakaway republics as independent states on August 26 after a five-day war with Georgia, which had attacked South Ossetia to bring it back under central control. Nicaragua has so far been the only other country to recognize the republics.
A member of the Belarusian legislature's international committee confirmed to RIA Novosti that Abkhazia and South Ossetia had approached Minsk with recognition requests.
Belarusian President Alexander Lukashenko, whose country has been trying to establish a union with Russia and is dependent on Russian energy supplies, said earlier he would back parliament if it chose to recognize the breakaway regions.
South Ossetia and Abkhazia have been given observer status in parliamentary sessions of the Russia-Belarus Union State.
The Caucasus conflict is the focus of a series of international talks being held in Geneva.
Abkhazia and South Ossetia have been de facto independent republics since they broke away from Georgia after the bloody post-Soviet conflicts in the early 1990s.