In a joint statement on Friday, the US, UK, Turkey and other coalition members said Russian strikes would "only fuel more extremism".
Russia, which according to witnesses launched fresh strikes on Friday, says it is targeting Islamic State (IS).
A senior Russian official says strikes could last for three to four months.
Alexei Pushkov, the head of the foreign affairs committee in Russia's parliament, added that the US had only "pretended" to bomb IS and promised that Russia's campaign would be much more effective.
The Russian air force began air strikes in Syria on Wednesday.
The Syrian military said Russia had carried out a total of 18 air strikes since Thursday evening. It said several of these were in Aleppo, Hama and Idlib, provinces with little IS presence.
Communications towers belonging to the Free Syrian Army - forces opposed to President Assad which have received American training and supplies - were destroyed in a Russian air strike in Aleppo.
The Russian defence ministry said it had attacked the IS stronghold of Raqqa on Thursday.
Source: BBC
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