Google and Facebook owner Meta should be held responsible for "inciting war", Russia's foreign ministry has said, according to the Interfax news agency and reported by Reuters.
The state communications agency Roskomnadzor also demanded that overseas internet services stop discriminating against Russian media.
It comes as internet giants try to restrict the sharing of Russian propaganda outside its borders but attempts to let ordinary Russians continue to access the services.
Meta's Nick Clegg said the company will continue to work closely with world governments on the issue.
"We have received requests from a number of governments and the EU [European Union] to take further steps in relation to Russian state-controlled media.
"Given the exceptional nature of the current situation, we will be restricting access to RT and Sputnik across the EU at this time," he wrote.
However the company won't shut down access to the platform in the country as it says it can also be used in positive ways.
"The Ukrainians have also suggested that we remove access to Facebook and Instagram in Russia.
"However, people in Russia are using FB and IG to protest and organise against the war and as a source of independent information.
"The Russian government is already throttling our platform to prevent these activities. We believe turning off our services would silence important expression at a crucial time."
YouTube has also announced it has banned access to Russian state media across Europe.
"It'll take time for our systems to fully ramp up," a spokesperson for the company said.
"Our teams continue to monitor the situation around the clock to take swift action."
Meanwhile Google, Meta, Twitter and other tech firms are facing punitive measures in Russia after failing to adhere to a law signed by President Vladimir Putin last July.
Foreign social media companies with more than 500,000 daily users were obliged to open local offices in the country and those failing to do so could face restrictions or even be banned from operating.
The companies also had to be registered with Roskomnadzor.
Apple and Spotify complied with the requirements ahead of the end-of-February deadline before restrictions, including the banning of selling advertisements, would begin.
TikTok, Zoom, Twitter, Meta and Google had yet to establish a local office according to the Russian government's website.
Clegg said Meta had been in protracted discussions with Roskomnadzor and were looking to comply with the law where the company felt "we can in good conscience".