Indian Prime Minister Manmohan Singh in a letter to Putin commended what he called "the Russian forces' measured response."
The Chinese Foreign Ministry also said it supports Russia's handling of the crisis and said hostage taking was an "atrocious terrorist" activity.
Australian Prime Minister John Howard condemned the hostage takers as deprived, obscene, and cruel.
Many other countries, including the United States, have condemned the hostage taking.
The European Union has asked Russia for a detailed account of the hostage taking in the wake of the shootout during which most of the casualties appear to have been suffered.