In March, thousands of people protested in Moscow against the law.
A law introducing new controls on the Internet came into force in Russia amid concerns that it could be used by the government to silence its critics.
In theory, the "sovereign internet" law gives employees broad powers to restrict traffic on the Russian web.
The Kremlin said the law will improve cyber security. A spokesman said users would not notice any changes.
Critics fear the Kremlin will try to build a similar Internet firewall to China.
Experts say it is unclear how the powers of the law can be used or how effectively they can be implemented in the face of technological challenges and high costs.
What is the law?
It gives the Kremlin the possibility to disconnect connections in Russia or completely to the world network "in case of emergency". It is up to the government to decide what constitutes a threat and what actions to take.
The law requires Internet service providers to install network equipment that can identify the source of traffic and filter content. In practice, this will allow the telecommunications observer Roskomnadzor to be more effective at lockout locations.
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Russia is trying to direct the country's traffic and web data through state-controlled points, reducing its reliance on foreign servers over which it has less control. Supporters say this is to protect the system from attacks from abroad.
To help with this project, the country is working on developing its own network address books to operate almost autonomously, although this work will not take effect until 2021.
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How Russia wants to control the internet
US intelligence said Russia used the Internet to interfere with the 2016 US presidential election, a claim Moscow denies.
This is the latest in a series of stricter Internet laws passed by Russia. Earlier this year, parliament passed two bills banning the "disrespect" of authorities and the spread of what the government considered "false news."
Why are there concerns?
Activists say the law is an attempt to increase censorship, based on Internet law that already reduces freedom of expression and privacy.
"Now the government can directly censor the content or even turn Russia's internet into a closed system without telling the public what they are doing or why, "said Rachel Denber, deputy director of Human Rights Watch in Europe and Central Asia.
The law, observers say, allows the government to block content without court consent and leaves users unaware of what information is being blocked and why.
Christian Mihr of Reporters Without Borders said: "[The law] proves that the Russian leadership is ready to put all network infrastructure under political control to cut off the flow of digital information as needed. "
In March, thousands of people protested in the capital, Moscow, against the law.