In the 2004 presidential elections, more than 3 percent of voters ticked the "against all" box on ballot papers.
Lawmakers said the move would encourage voters to be more engaged in politics.
Critics say the legislation deprives people of the right to publicly register their disapproval of candidates running in an election.
The legislation still needs to be approved by the upper house and signed by President Vladimir Putin.
(compiled from agency reports)
RFE/RL Russia Report
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