President Trump's former top advisor, Steve Bannon, has been suspended from Twitter over the "glorification of violence" amid the election aftermath.
Mr Bannon said a re-elected Mr Trump should fire the top infectious disease expert and the FBI director, and called for violence against them.
It comes as the tech firms continue a clampdown on misinformation.
Facebook has shut down a large group which alleges fraud, and announced new measures to amplify genuine results.
Mr Bannon, once widely thought of as one of the most powerful men in Washington, served as the boss of Mr Trump's 2016 campaign, and as a top presidential advisor for the first several months of his presidency.
On Thursday, he posted a video podcast to Facebook, YouTube and Twitter, in which he said both Dr Anthony Fauci - the face of the country's fight against coronavirus - and FBI Director Christopher Wray, should be fired after Mr Trump's re-election, but also said they should be subjected to violence.
President Trump has expressed frustration with both men, clashing with Dr Fauci over the pandemic, and with Mr Wray over what he sees as a failure to investigate his opponent, Joe Biden.
Facebook and YouTube both removed the video, but Twitter issued an outright suspension of Mr Bannon's "war room pandemic" account, for violating its policy on the glorification of violence.
The account has been permanently suspended, rather than banned for a limited amount of time, Twitter said in a statement.
President Trump, meanwhile, had another of his tweets hidden and labelled by Twitter after falsely claiming victory and alleging the existence of "illegal votes".
The President responded by tweeting: "Twitter is out of control".
Facebook 'demotes' some content
The Stop the Steal Facebook group had about 350,000 members when the social media giant removed it, something the social network admitted was an "exceptional" measure. It did so because it was "creating real-world events" and "we saw worrying calls for violence from some members of the group", Facebook said.
The social network is now taking further measures to restrict the flow of "inaccurate claims" in order "to keep this content from reaching more people".
"These include demotions for content on Facebook and Instagram that our systems predict may be misinformation, including debunked claims about voting. We are also limiting the distribution of live videos that may relate to the election on Facebook," the firm said in a statement.
Once Reuters and a majority of independent decision desks at major media outlets, including ABC, CBS, Fox, NBC, CNN and AP project a winner, we'll update the notifications running across the top of Facebook and Instagram with the projected winner of the election. pic.twitter.com/5asIe2hZip— Facebook Newsroom (@fbnewsroom) November 6, 2020
As President Trump continues to allege, without evidence, that widespread voter fraud took place, Facebook also said it would alter its election banner notifications and spread news of the projected winner, once a majority of independent outlets projected the result.
The same notice will be put on posts from both candidates.
Trump's 'special treatment' could end
Separately, Bloomberg reports that Twitter will remove the "special treatment" it affords President Trump as a world leader, in the event of Joe Biden winning the presidency.
Twitter has specific rules for world leaders, which means it will not ordinarily ban them for the same offences for which it would ban ordinary users. Twitter argues that such posts - even when violating its rules - are sufficiently newsworthy to stay up, with a handful of exceptions.
Instead, Twitter can label the post of a world leader, hiding it from view and restricting engagement - but leaving it viewable to anyone who clicks through a warning message about the content.
It has repeatedly done this to Mr Trump's tweets, leading to high-profile arguments with the president and his supporters.
But Mr Trump would return to the status of a regular user if he loses the election, Bloomberg reported - meaning that his tweets could be deleted outright or his account suspended, for policy violations.