Russia's Foreign Ministry spokeswoman Maria Zakharova also said on Thursday Russia was considering hitting the US for the deadline.
On RT's English language site, Simonya described the timeline as a "cannibalistic deadline", and wrote: "We believe that the demand does not only go against the law, and we will prove it in court - the demand is discriminative, it contradicts both the democracy and freedom of speech principles".
The Duma is obliged to give its laws two preliminary approvals before passing them, which Volodin said could happen next week.
Vyacheslav Volodin, speaker of the lower house of Russia's parliament, the State Duma, charged deputies with updating existing legislation after state-controlled Russia Today (RT) television was ordered by Washington to register as a "foreign agent" by Monday.
Russian Federation in 2012 passed a controversial law that requires foreign funded non-governmental organizations to register as foreign agents.
The Russian media outlets would have to register under the Foreign Agents Registration Act, which requires persons acting in "political or quasi-political capacity" for foreign interests to disclose information, funding and activities.
USA government-sponsored Radio Free Europe/Radio Liberty (RFE/RL) said last month Moscow had threatened to brand their Russian language service projects "foreign agents" in retaliation for US pressure on RT.
"These are not media, but propaganda tools with 100 percent funding from the US budget", Pushkov was quoted as saying.
Nikolov noted that foreign agent status implies a wide range of measures by the USA authorities, but no one knows what exactly can follow after this status is acquired.
"Every media now has its own pages in social networks, which also publish their news, articles and videos". Simonyan said the head of RT's USA subsidiary risked detention and the organization's bank accounts could be frozen if it didn't register.
Russian President Vladimir Putin signaled that he would sign such a law last month, when he told a conference of foreign policy scholars that Russia would respond immediately and reciprocally to "any efforts to limit our mass media". The decision came in the wake of investigations into Kremlin attempts to interfere in the 2016 US presidential election.
"Blatant pressure on the Russian mass media confirms that the United States pursues the course of deliberately hurting our relations", the statement said.
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.