But Sergei Bagapsh, Abkhazia's president, said the "size and number of population doesn't matter," according to the RIA news agency.
"Nauru is a member of the United Nations," he said.
Kommersant, a Russian daily newspaper, reported that Nauru had requested $50m in economic aid from Moscow ahead of the agreement.
But it has not been confirmed whether Russia, the main ally and sponsor of the breakaway region, would reward Nauru for the move.
The Kremlin agreed lucrative arms and energy deals with Venezuela and Nicaragua following their recognition of Abkhazia's independence.
Nauruan representatives also visited another breakaway region, South Ossetia, over the weekend and promised to consider recognising it as independent, the Associated Press news agency reported.
Abkhazia rejected Georgia's rule soon after the break-up of the Soviet Union in 1991, and broke away from Tbilisi in 1993 after a 13-month war.
Georgia continues to maintain that both Abkhazia and South Ossetia are part of its sovereign territory.