"Russia will be defeated," IS spokesman Abu Mohamed al-Adnani said in an audio recording posted online, calling on "Muslims everywhere to launch jihad against the Russians and the Americans."
Adnani said the United States was weak and unable to fight the jihadist group and using Iran and Russia to strengthen its position in Syria.
The United States is willing "to forge an alliance with the devil," he said.
In contrast "the Islamic State is today stronger than ever", Adnani added.
Russia, a key ally of the Syrian regime of President Bashar al-Assad, began its own bombing campaign on September 30.
In the recording Adnani also warned other rebel groups fighting the Syrian regime against confronting IS.