The MPs voted to adopt amendments to recognise a media outlet as a foreign agent in case this media outlet is funded from overseas.
The OSCE's media watchdog said on Thursday moves by the United States and Russian Federation to force some foreign media to register as "foreign agents" were unacceptable and unsafe.
A source in the Russian Justice Ministry told Sputnik on Wednesday that Radio Free Europe/Radio Liberty (RFE/RL) and Voice of America (VOA) received notifications about their possible recognition as foreign agents in Russia.
Russian Media has faced increasing pressure in the United States over the last few months amid multiple allegations of its attempts to influence the country's public opinion, especially during the 2016 presidential campaign.
According to Levin, the U.S. used its legislation against Russian journalists to "complicate as much as possible the conditions for their efficient work in the United States with the aim to restrict free competition on the media market".
It specifies that the final decision in classifying mass media outlets as foreign agents should be made by the Justice Ministry.
France says Saudi coalition must boost aid efforts to Yemen
Saudi Arabia has since said that aid can go through "liberated ports" but not Houthi-controlled Hodeidah, the conduit for the vast bulk of imports into Yemen.
It has vowed to retaliate by imposing restrictions on some foreign media operating in Russian Federation.
A third reading is required before the law passes to the upper house for approval.
He has been fiercely critical of United States measures towards Russian media, but he has not given wholehearted support to the draft legislation, saying at the weekend it "might be a little too harsh".
This measure was a response to the demand of the US Department of Justice to RT America, a US branch of the Russian television company, to register as a foreign agent.
A Russian law adopted in 2012 forces NGOs that have global funding and whose activities are deemed "political" to undergo intensive checks and label themselves as "foreign agents" on paperwork and statements.
They also have to apply for inclusion in a government register, submit regular reports on their sources of funding, on their objectives, on how they spend their money, and who their managers are. Moscow vowed to act swiftly in response to what it claims is a clampdown on Russian media in the U.S.