The broadly phrased bill leaves it to the Russian government to decide which foreign media outlets would be designated as foreign agents, but does not say how the determination would be made.
The proposal, in retaliation for Kremlin-backed broadcaster RT being told to register as a foreign agent in the U.S., has been approved at the lower house of parliament.
"We are talking about an opportunity for the executive-power bodies to take mirror measures against countries that are infringing upon Russian journalists' freedom of action and expression", RIA Novosti quoted Tolstoy as saying. "Every time, Russian Federation is going to take hard response measures".
Russian officials described the measure as a tit-for-tat response to last week's move from Washington.
RT television, which is funded by the Kremlin to give a Russian point of view on global affairs, confirmed Monday it has registered as a foreign agent in the United States, meeting a deadline from the US Department of Justice. Many US politicians accused the two Russian outlets of meddling in the 2016 US presidential election.
Amnesty International said the bill was an attack on media freedom. Any information they publish has to include a mention that the source of the information is a "foreign agent", according to the 2012 law.
It was not immediately clear which steps would be taken towards media in Russian Federation.
It states that such entities can be "recognized as foreign mass media executing the functions of a foreign agent if they receive monetary funds or other property from foreign states, government agencies, foreign-based and worldwide organizations, foreign citizens and persons without citizenship or any other persons acting on behalf of foreign citizens and organizations", according to TASS. Since then, they are requested to feature the label on their paperwork, statements, and other material.
USA intelligence officials accuse the Kremlin of using Russian media organisations it finances to influence US voters, and this week Washington required Russian state broadcaster RT to register a US -based affiliate company as a "foreign agent".
They can also be subjected to spot checks by authorities to make sure they comply with the rules.
With all 414 lawmakers present on Wednesday voting in favor of the amendment, the bill was officially endorsed by the 450-seat parliament. The Kremlin spokesman, Dmitry Peskov, said it was too early to say how tough the law would be because the draft did not spell out how it would be applied in practice.