“The companies will either have to localise the databases within a certain period of time, which I suppose will be about nine months, or they will be punished,” Roskomnadzor head Alexander Zharov was quoted as saying by Xinhua news agency on Tuesday.
He expects Twitter and Facebook representatives to meet with Roskomnadzor officials in Moscow by the end of February to discuss the issue.
Russian legislation requires Internet service providers to store and process personal data of Russians on the territory of Russia.
Roskomnadzor has the right to impose fines on or even block Internet companies for their violations.
In December, it fined Google 500,000 rubles (around USD 7,625) for failing to remove search links to banned information.
Last year, Roskomnadzor attempted to block instant messaging app Telegram in Russia due to its refusal to provide user data, but failed for technical reasons.