The opposition came in a statement released by the Shanghai Cooperation Organization on the final day of its summit in Beijing, China's official Xinhua news agency reported.
In the statement, the countries called for "dialogues that respect Syria's sovereignty, independence and territorial integrity," CNN reported.
The statement came as U.S. Secretary of State Hillary Clinton said Thursday in Istanbul, Turkey -- where she was attending a counterterrorism conference -- that "Syria will not, cannot be peaceful, stable or certainly democratic until [Syrian President Bashar] Assad goes."
U.N. Secretary-General Ban Ki-moon said the "dangers of full-scale civil war are imminent and real" in Syria and urged the government and opposition to end the violence.
The four former Soviet republics -- Kazakhstan, Kyrgyzstan, Tajikistan and Uzbekistan -- joined Russia and China in opposing military intervention or forced regime change in Syria.
The leaders of the six SCO countries said they oppose military intervention in response to Iran's nuclear program.
"We believe any attempts to resolve the Iranian issue by force are unacceptable," the SCO statement said. "Such attempts could lead to unpredictably serious consequences, which would threaten stability and security in the region and the entire world."
Western leaders suspect Iran is attempting to develop a nuclear weapon. Iran says its nuclear program is for peaceful purposes only.