LONDON – Russia is putting increasing pressure on Google, Twitter and Facebook to cope with Kremlin internet raids or risk restrictions in the country as governments around the world challenge corporate principles of online freedom.

Russian internet regulator Roskomnadzor recently increased its demands on Silicon Valley companies to remove online content it believes is illegal or to restore blocked pro-Kremlin material. The warnings have come at least weekly since Facebook, Twitter and Google services were used as an aid to protests against the Kremlin in January. If companies fail to comply, they face fines or access to their products can be restricted.

The most recent clashes came this week when Roskomnadzor asked Google on Monday to block thousands of unspecified illegal content as it would slow down access to the company’s services. On Tuesday, a Russian court fined Google 6 million rubles, or about $ 81,000, for not removing any other content.

On Wednesday, the government ordered that Facebook and Twitter should save all data on Russian users in the country by July 1 or be fined. In March, authorities made it difficult for people to see and send posts on Twitter after the company failed to remove content the government deemed illegal. According to Roskomnadzor, Twitter has since removed around 6,000 posts to meet the orders. The regulator has threatened similar penalties against Facebook.

Russia’s campaign is part of a wave of measures by governments around the world to test how far they can go to censor the internet in order to maintain power and quell dissent. Police visited Twitter’s New Delhi offices on Monday to demonstrate violence. No staff were in attendance, but India’s ruling party is increasingly angry at the perception that Twitter sided with its critics during the coronavirus pandemic.

In Myanmar, Poland, Turkey and elsewhere, heads of state and government are also tightening internet controls. In Belarus, President Aleksandr G. Lukashenko signed a law this week banning live streams of unauthorized protests.

“All of these guidelines will lead to the creation of a broken Internet in which people have different access to different content,” said Jillian York, Internet censorship expert at the Electronic Frontier Foundation in Berlin.

The battle for online language in Russia has important ramifications as internet companies have been viewed as a shield against government censors. The latest moves are a big change in the country where the internet, unlike television, has remained largely open despite President Vladimir V. Putin’s close influence on society.

That has changed as Russians have increasingly used online platforms to speak out against Putin and organize and exchange information. Russian officials have followed China’s Great Firewall and pledged to build a “sovereign Internet,” a legal and technical system to block access to certain websites and shield parts of the Russian Internet from the rest of the world.

“What is happening in Russia foreshadows an emerging global trend when censorship is just a tool in the ultimate battle of writing the rules that major technology platforms must follow,” said Sergey Sanovich, a Princeton University researcher who focuses on Internet Focused on censorship and social media governance.

Roskomnadzor did not immediately respond to a request for comment. In an interview this week with Kommersant, a leading Russian newspaper, Andrey Lipov, the boss of Roskomnadzor, said that slowing down access to Internet services was one way of forcing companies to comply with Russian laws and purchase orders. Mr Lipov said the aim is not to block their services altogether.

Google declined to discuss the situation in Russia, saying it has received government inquiries from around the world which it discloses in its transparency reports.

Facebook wouldn’t discuss Russia either, but said it restricts content that violates local laws or its terms of use. “We always try to keep the voice for most people,” said a spokeswoman.

Twitter said in a statement that it removed content flagged by Russian authorities that violated its policies or local law.

“Access to a free and open Internet is an essential right for all citizens,” said Twitter. “We remain committed to providing safe service to account holders around the world, including Russia.”

Anastasiia Zlobina, a Human Rights Watch researcher who focuses on Russian internet censorship, said the government’s actions threaten the future of American internet services in the country. A turning point was when YouTube, Facebook and Twitter were used in protests in support of opposition leader Alexei A. Navalny after his arrest in January. The demonstrations were the biggest disagreement against Putin in years.

“This mobilization took place online,” said Ms. Zlobina.

The Russian government has portrayed the tech industry as part of a foreign campaign to meddle in domestic affairs. The authorities have accused the companies of blocking Kremlin-friendly online accounts while strengthening the opposition. The platforms are also places of refuge for child pornography and drug sales.

According to researchers at the University of Michigan, Twitter became the first major test of Russian censorship technology in March when access to its service was slowed down.

To resolve the conflict, a Twitter manager met with Russian officials at least twice, according to the company and Roskomnadzor. The government, which threatened to ban Twitter entirely, said the company eventually fulfilled 91 percent of its shutdown requests.

Other internet companies are also affected. Last month, TikTok, the popular social media platform operated by Chinese company ByteDance, was fined 2.6 million rubles, or about $ 35,000, for not removing posts encouraging minors to participate in illegal demonstrations . TikTok did not respond to a request for comment.

The fines are small, but the fines are bigger. The Russian government can increase fines for repeat offenses to up to 10 percent of a company’s revenue and, perhaps more importantly, the authorities can disrupt their services.

Perhaps the biggest target was Google. YouTube was an important way for government critics like Mr. Navalny to share and organize information. In contrast to Facebook and Twitter, Google has employees in Russia. (The company wouldn’t say how many.)

In addition to this week’s warning, Russia has requested that Google lift restrictions restricting the availability of some content from state media outlets such as Sputnik and Russia Today outside of Russia.

The Russian antitrust agency is also investigating Google over YouTube’s video blocking policy.

Google is trying to use the courts to combat some actions by the Russian government. Last month she sued Roskomnadzor over an order to remove 12 YouTube videos related to opposition protests. In another case, the company appealed a decision instructing YouTube to re-record videos from Tsargrad, a nationalist online TV channel that Google abolished for alleged violations of American sanctions.

Joanna Szymanska, a senior program officer for Article 19, an internet freedom group, said Google’s recent lawsuit against the YouTube shutdown orders would affect what other countries would do in the future, even if the company were likely to lose in court. Ms. Szymanska, who is based in Poland, urged tech companies to be more transparent about what content to delete and what assignments to keep.

“The Russian example is used elsewhere when it works well,” she said.

Adam Satariano reported from London and Oleg Matsnev from Moscow. Anton Troianovski contributed to reporting from Moscow.