Russian President Dmitry Medvedev says Russia has united support from China and Central Asian allies for its actions in Georgia.
He says that should send a "serious signal" to the West.
Mr Medvedev made his remarks at a summit of the Shanghai Cooperation Council, grouping Russia, China and four former Soviet states in Central Asia.
Britain wants engagement
British Foreign Secretary David Miliband has called on the European Union and Nato to initiate "hard-headed engagement" with Russia in response to its actions in Georgia.
In a speech in Ukraine's capital, Kiev, he urged them to bolster their allies, rebalance the energy relationship with Russia and defend international law.
Russia recognised the independence of Georgia's two breakaway regions, South Ossetia and Abkhazia, on Tuesday.
Moscow's fellow G8 members have condemned its actions in Georgia.
"We, the foreign ministers of Canada, France, Germany, Italy, Japan, the United States and the United Kingdom, condemn the action of our fellow G8 member," the group of seven of the world's leading industrialised nations said.
"We deplore Russia's excessive use of military force in Georgia and its continued occupation of parts of Georgia."
Ukraine's President Victor Yushchenko has said his country is a hostage in a war waged by Russia against countries in the old Soviet bloc.
He told Mr Miliband that the brief conflict between Georgia and Russia earlier in August had exposed serious weaknesses in the powers of the United Nations and other international bodies.
He called for Ukraine's defences to be strengthened and said his country would consider increasing the amount of money Russia pays for the lease of the port of Sevastopol, where it stations its Black Sea Fleet.
The Russian government responded to Mr Miliband's criticism, saying Moscow saw no threat of a new Cold War.
Meanwhile, Georgia's former president Eduard Shevardnadze says Russia will live to regret its recognition of rebel regions.
Mr Shevardnadze, who was also a foreign minister of the former Soviet Union, says Moscow's move would "encourage separatist movements within ethnically diverse Russia."
The prosecutor general of Georgia's breakaway region of South Ossetia says 1,692 people were killed in Georgia's attack this month.