The rally gathered around 15,300 people, according to White Counter, an NGO that counts participants at rallies. On the other hand, the Moscow police estimated the number to be around 6,500.
There were pockets of violence during Sunday's protest with a few demonstrators being detained.
The legislation has already been approved by Russian lawmakers, but has to pass through a couple of other stages before it becomes law.
The legislation, known as the Digital Economy National Program, will be up for a second vote this month, after which it'll go to the upper house of the parliament and ultimately President Vladimir Putin for signing. "It reminds me of my youth, and I don't want this for my children and my grandchildren". "We are part of the civilized world", a statement from the Libertarian Party said. There were protests previous year when the encrypted messaging app Telegram was banned by authorities who said it was being used by terrorists.
The government claims that this will improve cybersecurity and prevent foreign meddling in Russian affairs, yet many have deemed it an online "iron curtain" that could be used to suppress dissenting voices. It proposes the establishment of a center to "ensure and control the routing of internet traffic" in the country.
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Today's big tech companies have too much power - too much power over our economy, our society, and our democracy. She used the flap to warn that it was unsafe for cyberspace to by "dominated by a single censor".
The goal of the bill is "total censorship", it said.
Advocates say the bill is meant to address concerns that Russian Federation could be cut off if the United States applies a new cybersecurity doctrine in an offensive maneuver.
Nikolai Lyaskin, an aide to opposition leader Aleksei Navalny, called the bill yet another step by the authorities to "tighten the screws" on Internet freedom, and urged the Russians to rally against "this madness".
Earlier this week, the Duma passed a bill penalizing media outlets as well as individuals that publish fake news and insult the government online.
February's bill passed in the Russian parliament on the first reading out of three.