The bill, which would to increase fines to up to 300,000 rubles ($9,000) for individuals who violate rally rules, cleared the final parliamentary hurdles Wednesday, now needing only the president's signature to become law.
In a country where the average annual income is several hundred dollars less than the maximum fine, the bill has become a controversial topic.
Only 17 percent in the Levada poll approve of the penalties to be enacted in the bill, while 26 percent said fines were a good idea, but those proposed in the bill were too high, Vedomosti reported.
About 70 percent of Russians have heard about the May 6 opposition rally that ended with violence by both demonstrators and police, prompting the creation of the bill. Forty-six percent said riot police reacted too harshly, while 4 percent said police were "too soft."
The poll revealed that 67 percent think Putin should enter into a dialogue with opposition protesters, but 45 percent said they thought the would try to stamp out opposition protests, up from 32 percent in a January poll.