The appeal was made at a Monday meeting of the Abkhazian parliament.
Ireland became an independent republic after many years of struggle under British rule.
“Just like Ireland, Abkhazia has finally acquired long-awaited independence and recognition at the cost of enormous efforts," the parliament’s appeal said.
"The Irish Free State, which eventually became the Republic of Ireland, was de-facto independent for a long time, but remained unrecognised. Ireland was the only unrecognised country in Europe until the world's largest country recognised a free parliament of Ireland. And that country was Russia."
“Abkhazia is in the same situation today. For 15 years Abkhazia existed as an independent, although unrecognised, state.”
Sukhum believes that Abkhazians have all the legal and historic conditions for independent development.
The parliament’s statement says: "Relations between the Georgian and Abkhazian nations went through serious trials during the past century, which proved that Abkhazians could not live together with the Georgians in a single state."
According to deputies, Abkhazia has formed its own administrative and political system, a legislative system and a market-oriented economy. The republic has independent courts and civil society and respects human rights.
In its appeal to the Belarusian parliament, Sukhum thanked Minsk for its support during the conflict with Georgia.
In August, Russia recognised the independence of Abkhazia and South Ossetia. That followed a military conflict between Georgia and its two breakaway regions. Later the two states were recognised by Nicaragua.