Russia's media authority Roskomnadzor sent letters to the U.S. tech giants this week asking them to comply with internet rules.
Moscow's "blogger law" requires that bloggers with more than 3,000 daily readers publish content under their real names and register with the authorities.
With that in mind, Roskomnadzor has asked Google, Twitter and Facebook to hand over the names of relevant bloggers and to remove blog content "recognized as extremist information" by the Russian Attorney General.
"Such correspondence is regular in dealing with foreign Internet companies," Vadim Ampelonskiy, press-secretary for Roskomnadzor, told CNBC on Friday via email.
"Usually after sending official requests and letters, we can see some positive movements and progress in communication. Roskomnadzor hopes this time all the companies will respond again and will fulfill those requirements, which were asked many times before," he added.
The spokesperson told Reuters that the encryption around the companies' websites meant the authorities couldn't block specific pages holding particular content that violated the rules and instead would have to block the whole service.
Twitter and Facebook have been popular platforms for critics of Russian President Vladimir Putin, so the Moscow move has not come as a surprise to the companies and industry-watchers. However, given that Facebook also operates Instagram and Google has numerous properties, any blockade has the possibility of affecting several sites.
Russia has been increasingly tightening its internet laws and last year passed legislation that allowed authorities to block sites without a court order. Critics have slammed the Kremlin's moves as censorship.
Facebook publishes government requests for data on its website and says "each and every request we receive is checked for legal sufficiency and we reject or require greater specificity on requests that are overly broad or vague". In 2014, it received two requests for data from the Russian government, both of which were rejected.
Twitter deals with government requests in the same way and in 2014, received 108 requests from Russia, none of which were granted. The micro-blogging site also said it received 89 requests to remove content but only complied with 13 percent of those.
"We denied several requests to silence popular critics of the Russian government and other demands to limit speech about non-violent demonstrations in Ukraine," according to a statement on Twitter's website.
In 2014, Google received 134 requests for data about users and complied with 5 percent of those, according to the company's Transparency Report online.