The move follows Moscow's decision to recognise the republics' independence after Georgia attempted to gain control of South Ossetia by force last month.
Nicaragua became the second country to recognise their independence.
Meanwhile, the Belarusian president Aleksandr Lukashenko has also spoken about acknowledging South Ossetia and Abkhazia as independent states.
He said a decision on the issue would follow a parliamentary election at the end of this month.
Belarus has a history of good relations with Abkhazia, and Lukashenko said he was keen to express his full support for Russia's position.
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