Moscow, an ally of Syrian leader Bashar al-Assad, has been staging bombing raids in Syria since September 2015.
Forty-eight percent of Russians were concerned that "heightened tensions in relations between Russia and the West could grow into World War III," according to a poll conducted by independent pollster Levada Centre last week.
That figure was up from 29 percent in July this year.
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Moscow's air strikes have negatively affected the way Russia is perceived internationally, 32 percent said, up from 16 percent in November.
Nevertheless, 52 percent of Russians said they back Moscow's air strikes, while 26 percent said they opposed them.
Asked whether Russia should continue "intervening in what is going on in Syria," 49 percent said yes, while 28 percent said no.
Western powers and rights groups have accused Syrian and Russian forces of carrying out indiscriminate attacks on civilian infrastructure in the country, particularly around the former economic powerhouse Aleppo, parts of which have been reduced to rubble.
Moscow announced on October 18 it was halting strikes on Aleppo in a moratorium that has so far lasted 14 days.