Updated

Sen. Josh Hawley, R-Mo., introduced legislation Wednesday to give Americans the ability to sue major tech companies like Facebook, Google and Twitter if they engage in selective censorship of political speech.

The Limiting Section 230 Immunity to Good Samaritans Act, cosponsored by Sens. Marco Rubio, R-Fla., Mike Braun, R-Ind., and Tom Cotton, R-Ark., would stop such companies from receiving immunity under section 230 of the Communications Decency Act, unless they update their terms of service to promise to operate in good faith.

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“For too long, Big Tech companies like Twitter, Google and Facebook have used their power to silence political speech from conservatives without any recourse for users,” Hawley said in a statement. “Section 230 has been stretched and rewritten by courts to give these companies outlandish power over speech without accountability. Congress should act to ensure bad actors are not given a free pass to censor and silence their opponents.”

The bill would allow users to sue companies for breaching that contractual duty of good faith, and it would make them pay $5,000 plus legal fees to each user who prevails in a case against them.

On a separate track -- reflecting renewed pressure on these companies out of Washington -- the Justice Department is recommending that lawmakers consider new legislation that would hold tech giants liable for content posted online. Any such legislation would roll back legal protections the online platforms have possessed for decades.

The DOJ proposed extensive changes to the law in question, Section 230, in a report Wednesday afternoon. The report does not call for repealing the statute entirely, but for rolling back immunity for platforms that facilitate criminal activity and for those that don't take action when notified of "specific criminal material or activity."

This comes after President Trump signed an executive order this month that interprets Section 230 as not providing statutory liability protections for tech companies that engage in censorship and political conduct -- though DOJ officials say the department has been working on the legislative recommendations for months and they are not a direct result of Trump’s order.

"My executive order calls for new regulations under Section 230 of the Communications Decency Act to make it so that social media companies that engage in censoring any political conduct will not be able to keep their liability shield," the president said at the time.

The president's order, which also cuts federal funding for social media platforms that censor users' political views, came after Twitter took the unprecedented step of slapping a "misleading" warning label on two of Trump's tweets concerning the fraud risks of nationwide mail-in balloting.

Axios reported that the White House requested that Hawley target the liability shield that surrounds big tech companies.

The bill was introduced a day after NBC News reported on a Google crackdown against two conservative websites -- Zero Hedge and The Federalist.

NBC News initially claimed Google "banned" The Federalist and ZeroHedge from Google Ads for "pushing unsubstantiated claims" about the Black Lives Matter movement. Google later pushed back, claiming that The Federalist "was never demonetized.”

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"We worked with them to address issues on their site related to the comments section," Google said. "Our policies do not allow ads to run against dangerous or derogatory content, which includes comments on sites, and we offer guidance and best practices to publishers on how to comply."

A Google spokesperson reiterated to Fox News, "To be clear, The Federalist is not currently demonetized. We do have strict publisher policies that govern the content ads can run on, which includes comments on the site. This is a longstanding policy."

Fox News' Joseph Wulfsohn and Gillian Turner contributed to this report.