The bill must undergo two more readings in the Duma, be passed by the Federation Council, and be signed by President Vladimir Putin before it becomes law.
Supporters of the bill say the amendments will make voters act more responsibly when they cast ballots.
Vladimir Pligin, the chairman of the Russian State Duma's Committee for Constitutional Legislation, said the bill will encourage voters to make a choice.
"The entire spectrum of political views -- and it is not very large: the right, the left, the centrist views -- the entire spectrum of political views is fully represented by political parties working within the legal field of the Russian Federation," Pligin said.
Critics say the bill will result in fewer people turning out to vote. In previous elections, voting "against all" was seen as a protest against political parties.
A total of 352 deputies, well above the required majority of 226, backed the bill. Opposition parties voted against it.
COOPERATION, CONFLICT, CONFRONTATION: Relations between Russia and the West are notoriously volatile. "To see the kind of relationship that presidents Bush and Putin have developed and to see Russia firmly anchored in the West, that's really a dream of 300 years, not just of the post-Cold War era," then-national security adviser Condoleezza Rice said in May 2002.
But observers have increasingly called into question the extent of the shared values between Russia and the West, particularly on issues relating to the transformations going on in other former Soviet countries.
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