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"The law is compulsory for all," the head of Roskomnadzor telecoms watchdog Alexander Zharov told journalists in Moscow, quoted by Interfax news agency.
"We will work on getting Facebook to observe the law," Zharov said. "This will all happen in 2018 definitely."
A controversial law passed in 2014 requires foreign messaging services, search engines and social networking sites to store the personal data of Russian users inside Russia.
The law, which was fiercely opposed by the telecommunications industry, is an apparent move to pressure sites such as Facebook and Twitter into handing over user information.
"In any case we will either get the law carried out or the company will stop working in Russia, as unfortunately happened to LinkedIn," Zharov said.
"There are no exceptions here," he added.
Zharov's comments came after Facebook revealed that Russia-linked fake accounts paid for ads that may have influenced last year's US election.
Facebook said it was sharing its findings with the US authorities.
The threat of a ban also comes as Russia is gearing up for presidential elections in March next year.
The online platform allows him to bypass state television, which only gives him negative coverage.
"We understand very well that Facebook has a significant number of users in Russia, but on the other hand, we understand that it's not a unique service, there are other social media sites," said Zharov.