The third reading is seen as a formality, after which the amendments will have to be passed by the Senate and then be signed into law by President Vladimir Putin.
The law designating media outlets as foreign agents, passed by the State Duma on Wednesday, will allow Russia's authorities to immediately and symmetrically respond to the encroachment on the freedom of Russian media overseas, Kremlin Spokesman Dmitry Peskov told reporters.
The State Duma has passed an amendment, which allows the state to recognize foreign media receiving financing from overseas as "foreign agents" in third and final reading.
Non-compliant foreign organizations could be blocked without a court order in Russian Federation.
It also will likely be used to selectively target media from countries in conflict with the Kremlin, in particular if that conflict involves the state-funded television station RT, which used to be known as Russia Today. Moscow vowed to act swiftly in response to what it claims is a clampdown on Russian media in the U.S.
The bill will pass to the upper house which is expected to quickly rubber-stamp it next week before it goes to Mr Putin.
"This campaign looks like it's going to go on for a long time", Tolstoy said, referring to what he called pressure on Russian journalists overseas.
RT is accused of being part of Russia's alleged meddling in the USA election. "Every time, Russian Federation is going to take hard response measures". "We are listening carefully to the questions our colleagues in Congress are asking", he said, "and we have questions of our own".
This move became a response to the demand by the US Department of Justice that the US branch of Russia's RT television channel, RT America, should register as a foreign agent by November 13.
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. Any information they publish has to include a mention that the source of the information is a "foreign agent", according to the legislation. Foreign media that do not register when requested can lose the right to work in Russian Federation.