"The UN Charter sets forth the 'equal rights of nations large and small.' Russia's invasion of Georgia was a violation of those words. Young democracies around the world are watching to see how we handle this test," Bush said in his farewell speech to the UN General Assembly.
He said Washington would work with its NATO allies and with the European Union to defend Georgia's territorial integrity.
Russia came under strong criticism for Western powers in its five-day conflict with Georgia last month, which followed Georgia's August 8 attack on breakaway South Ossetia. Russia subsequently recognized South Ossetia, along with Abkhazia, as independent states.
French President Nicolas Sarkozy also singled out Russia for criticism in his speech to the assembly, saying Moscow "cannot compromise on the principle of states' sovereignty and independence, their territorial integrity."
The main focus of the UN General Assembly session was the ongoing global financial crisis.
In his speech, Secretary-General Ban Ki-moon warned that financial troubles in rich nations could harm aid to poor countries, and called on states to abandon their "uncritical faith" in market forces.
