The law has been criticized as a way for the Russian government to marginalize civil society institutions.
Volodin told Russian reporters the new measures, which would affect dozens of United States news organisations operating in Russia including CNN and Voice of America, could be adopted at first reading on Wednesday and at a third and final reading next Friday.
The Duma is obliged to give its laws two preliminary approvals before passing them, which Volodin said could happen next week.
Russian Federation is poised to list USA media outlets as "foreign agents" by extending legislation used to restrict the activities of civil society groups, in retaliation for an American order requiring state broadcaster RT to register for a similar status. "Since such decisions are being made on USA territory in relation to our TV channels, it will be right for us to respond to these actions".
It was not clear how this label would apply to US media and how it would potentially affect their work, or how many media outlets would be affected.
San Francisco-based social network Twitter has also angered Russian authorities when it accused RT and the Sputnik news outlet of interfering in the 2016 USA election and banned them from buying ads on its network.
The US Department of Justice has said the US branch of Russia's RT television channel, RT America, should register as a foreign agent before November 13, the network reported on its website on Thursday.
Twitter has already banned advertising from RT and Sputnik, another Russian news outlet.
She added: "We will continue to work and continue to fight this as long as it's possible".
"Reciprocal measures will be taken to impose the same limitations that Americans are trying to impose on Russian media based on the 1938 law on foreign agents", Tolstoi said.
"The Russian side has repeatedly warned that any measures limiting activity of the Russian mass media in the United States will inevitably trigger an immediate symmetrical response", the Russian embassy posted.
The Kremlin has even taken aim at privately owned CNN, which has been the subject of criticism from Russia, for what the government views as anti-Russian reporting.
The speaker of the State Duma, Russia's lower house, Friday asked the house committees to prepare a legislative response to the "U.S. pressure on Russian media".
"It will very much complicate the possibility of interviewing people because we will have to report this too", she said.
In its January report, US intelligence called RT "the Kremlin's principal worldwide propaganda outlet", saying it was part of "Russia's state-run propaganda machine", which had "contributed to the influence campaign by serving as a platform for Kremlin messaging".
The assessment also said RT America "has positioned itself as a domestic USA channel and has deliberately sought to obscure any legal ties to the Russian government, " but behind the scenes, "the Kremlin staffs RT and closely supervises RT's coverage, recruiting people who can convey Russian strategic messaging due to their ideological beliefs".
Human rights groups have condemned the label, who say it echoes Soviet-era attacks on dissidents.