DUSHANBE, Tajikistan — China and several Central Asian nations rebuffed Russia's hopes of international support for its actions in Georgia, issuing a statement Thursday denouncing the use of force and calling for the respect of every country's territorial integrity.

A joint declaration from the six-member Shanghai Cooperation Organization also offered some support for Russia's "active role in promoting peace" following a cease-fire, but overall it appeared to increase Moscow's international isolation.

Russia's search for support in Asia had raised fears that the alliance would turn the furor over Georgia into a broader confrontation between East and West, pitting the U.S. and Europe against their two main Cold War foes.

Russian President Dmitry Medvedev had appealed to the Asian alliance, which is made up of China, Russia and four ex-Soviet Central Asian nations, for unanimous support of Moscow's response to Georgia's "aggression."

But the alliance, which was created in 2001 to improve regional coordination on terrorism and border security, opted to take a neutral position and urged all sides to resolve the conflict through "peaceful dialogue."

"The participants ... underscore the need for respect of the historical and cultural traditions of each country and each people, and for efforts aimed at preserving the unity of the state and its territorial integrity," the alliance's statement said.

None of the other alliance members joined Russia in recognizing the independence claims of Abkhazia and South Ossetia.

Russian Prime Minister Vladimir Putin, in an interview with CNN, accused the U.S. of orchestrating the conflict in Georgia to provide a talking point in the American presidential campaign. The White House press secretary Dana Perino called the claims "patently false."

Russia's decision to recognize Georgia's separatist regions Tuesday sparked another storm of criticism from the West because both provinces make up roughly 20 percent of Georgia's territory. The West had already criticized Russia for what it calls a disproportionate use of force in fighting this month with Georgia, its small southern neighbor that wants to join NATO.

In Washington, State Department spokesman Robert Wood expressed satisfaction about the Asian group's statement, saying "it wasn't what I would call an endorsement of Russia's recognition of Abkhazia and South Ossetia."