It specifies that the final decision in classifying mass media outlets as foreign agents should be made by the Justice Ministry.
Legislator Leonid Levin said the bill will provide a tool for the Justice Ministry to designate worldwide media outlets as foreign agents.
Russian MPs backed amendments that would allow global media that receive financing from overseas to be classified as "foreign agents", RIA Novosti news agency reported, a measure previously used only against NGOs.
Once registered, they will face requirements now applied to foreign-funded non-governmental organisations.
The Moscow-based broadcaster has become a focus of the investigations into alleged Russian interference in the 2016 United States presidential election.
The bill will go to the upper house and then to President Vladimir Putin for signing.
Russian Federation has denied it interfered in last year's United States presidential election.
Mr Putin has criticised the U.S. demand regarding RT as an attack on freedom of speech and warned that Russian Federation would retaliate.
The motion was prepared by State Duma Speaker Vyacheslav Volodin and the heads of all four parliamentary caucuses.
Theresa May launches attack on Russian election 'meddling'
May said Russia's "illegal annexation of Crimea" was the first time since the Second World War that a sovereign nation has forcibly taken territory from another in Europe. "We know what YOU are doing as well".
The bill was passed unanimously with 414 votes in favour.
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.
"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.
"I would like to hope that it will only be used once and there will be no need for more retaliatory action", he added.
US-backed Voice of America and Radio Free Europe/Radio Liberty could be hit.
Russian Federation has moved closer to introducing a law that will allow the government to list any foreign media operating in the country as a foreign agent.
Companies will be forced to declare their finances, funding and staffing if the rules are implemented.
Amnesty International criticised the new bill as an attack on media freedom.
"Over the last couple of years, the Kremlin has been tirelessly building a media echo chamber that shuts out critical voices, both inside Russian Federation and from overseas".