Thousands of people have taken the streets in Moscow and similar demonstrations in two other Russian cities were called as the government plans to introduce tighter restrictions on the internet.
Last month, Russian parliament backed the controversial bill.
The government says the bill, which allows it to isolate Russia’s internet service from the rest of the world, will improve cyber-security.
However, campaigners say it is an attempt to increase censorship and stifle dissent.
Activists say more than 15,000 people gathered in Moscow on March 10, which is double the estimate given by the police.
Some protesters chanted slogans such as “hands off the internet” and “no to isolation” while others gave speeches on a large stage.
Opposition figures said that a number of protesters were detained in Moscow, but the police have not confirmed this.
The government says the so-called digital sovereignty bill will reduce Russia’s reliance on internet servers in the US.
The bill seeks to stop Russia’s internet traffic being routed through foreign servers.
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A second vote is expected later this month.
If it is passed, the bill will eventually need to be signed by President Vladimir Putin.
Russia has introduced a swathe of tougher internet laws in recent years. On March 7, parliament passed two bills outlawing “disrespect” of authorities and the spreading of what the government deems to be “fake news”.
Last year, campaigners took to the streets to protest the media watchdog’s attempt to shut down the encrypted messaging service, Telegram.
Russia’s main security agency, the FSB, said at the time that Telegram was the messenger of choice for “international terrorist organizations in Russia”.