The so-called "sovereign Internet" bill, which passed in the first reading in the lower chamber of Russia's parliament on February 12, faces two more votes in the State Duma before heading to the upper house.
Thousands of protesters gathered in Moscow on Saturday to rally against a draft law that aims to reconfigure the foundation of Russia's internet.
But an estimated 15,300 people protested at the weekend in Moscow and reportedly made speeches on a stage and chanted slogans such as "hands off the internet" and "no to isolation, stop breaking the Russian internet".
About 15,300 people demonstrated for Internet freedom on Sunday in Moscow, according to White Counter, a group that monitors the number of attendees at rallies. Moscow police put the numbers at 6,500.
"If we do nothing it will get worse", one protester told Reuters news agency.
Protests over the same internet regulation also took off in the southern city of Voronezh and the far east city of Khabarovsk.More news: Six Nations should consider relegation, says England head coach Jones
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The police detained several people, including RFE/RL's Russian Service correspondent Andrei Kiselyov. While these three protests were officially authorized by local police, the protest in St. Petersburg was held without the consent of authorities.
Russian Federation has in recent years attempted to curb internet freedoms by blocking access to certain websites and messaging services such as Telegram.
The legislation is part of a drive by officials to increase Russian "sovereignty" over its internet segment. The law also proposed to build a national Domain Name System which will allow the country's internet to continue to work despite being cut off from the global infrastructure.
The move was labelled by critics as the latest attempt to control online content under President Vladimir Putin, with some fearing the country is on track to completely isolate its network like in North Korea.
That decision was taken by Russian authorities after the app refused to give Russian state security services access to its users' secret messages by handing over encryption keys used to scramble the messages.