Legislator Leonid Levin said the bill will provide a tool for the Justice Ministry to designate global media outlets as foreign agents.
In the 450-seat State Duma, the lower house of parliament, 409 lawmakers voted on Wednesday to approve the legislation on second reading, with none against, according to TASS news agency.
Russian lawmakers have unanimously passed a bill targeting foreign news outlets in retaliation to the Kremlin-run news channel RT's registration as a "foreign agent" in the United States. In a statement, the Justice Department said the US legislation, the Foreign Agents Registration Act (FARA), merely informs the public without inhibiting "freedom of expression".
US-backed Voice of America and Radio Free Europe/Radio Liberty could be hit.
The bill was sent to Russia's upper house of parliament to be rubber-stamped before being submitted to President Vladimir Putin for final approval.
The law could require designated media outlets to disclose where they get their funding and how they spend it, though the bill does not specify on what basis foreign media would be compelled to register.
Tolstoy told parliament the amendments would not be automatically enforced, but would be selectively applied by the justice ministry. Foreign media that do not register when requested can lose the right to work in Russian Federation.
"I would like to hope that it will only be used once and there will be no need for more retaliatory action", he added.
The text of the amendment defines affected mass-media outlets as legal entities that are "registered in a foreign nation, or a foreign structure that operates without registering as a company, engaged in spreading printed, audio, audio-visual or any other content prepared for an unlimited group of people".
The bill serves as an amendment to the 2012 law that forced NGOs to adopt a "foreign agent" label if they receive funding from overseas. They will also face a similar responsibility for such NGOs for breaching this legislation.
The measures were introduced in response to a move by the U.S. Department of Justice to force RT America, linked to the Kremlin-backed RT, to register as a "foreign agent" after U.S. intelligence officials accused Russian Federation of seeking to influence the 2016 U.S. presidential election.
Amnesty International has warned the law will allow the Russian authorities "to tighten their stranglehold on press freedom".
The Moscow-based broadcaster has become a focus of the investigations into alleged Russian interference in the 2016 U.S. presidential election.