The measures, which are being prepared ahead of Russia´s presidential election in March, would be a huge blow to already tattered US-Russia ties.
State Duma speaker Vyacheslav Volodin charged deputies with updating existing legislation after state-controlled Russia Today (RT) television was ordered by Washington to register as a "foreign agent" by Monday.
Volodin told Russian reporters the new measures, which are likely to affect dozens of US news organisations operating in Russia including CNN and Voice of America, could be adopted at first reading on Wednesday and at a third and final reading next Friday.
Washington has been fighting what it calls a barrage of "fake news" from Russian media, including RT and the Sputnik news agency, which it says is aimed at interfering in US domestic politics.
This is not only financial documentation which entails dozens of questions," Volodin said, referring to requirements faced by "foreign agents" in the US. It is "the disclosure of all information," he added.
In a Facebook post, Tolstoy suggested that social networks would not have to register as foreign agents.
"This does not mean someone is impinging on Facebook, Twitter etc," he wrote.
"This does not mean someone is impinging on Facebook, Twitter etc," he wrote.
Russian telecoms watchdog Roskomnadzor, for its part, proposed blocking the websites of foreign media groups and nongovernmental organisations, without any need of a court order.
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