Under the act, Nauru is no longer eligible for financial support from the US government as it recognises two Georgian break-away regions as independent countries.
The act declares that Abkhazia and South Ossetia are Russian-occupied territories belonging to Georgia.
It also prohibits US representatives in international financial institutions from supporting programmes that violate Georgia's sovereignty.
Nauru, which has a population of about 10,000, refurbished its port with Russian aid money after it recognised the regions' independence from Georgia in 2009.
