Parliament's lower house, the State Duma, passed the bill in its third, and final reading Friday, but it needs to be approved by the upper house, the Federation Council, to become law.
Federation Council Speaker Sergei Mironov said: "Not just me, but many of my colleagues, oppose the logic of this bill."
He described as "dubious" arguments made by supporters of the bill who "believe it is unacceptable that a party with no realistic chance of making it into the State Duma gets registered and runs a campaign only to sling mud at everyone."
The new legislation is sponsored by the pro-Kremlin United Russia party, the ultranationalist Liberal Democratic Party and Rodina, who say it is designed to prevent "extremist practices" in election campaigning.
But the Communist Party opposes the bill, arguing that the abolition of the turnout threshold will make the country's electoral system "unviable" and incapable of reflecting the will of the people.