Social media firms suppressed conservative points of view, the president claimed without providing any evidence, before saying his administration would “strongly regulate [the companies] or close them down, before we can ever allow this to happen”.
Mr Trump advised the companies to “Clean up your act, NOW!!!!”.
It is unclear whether the president’s professed goal would be compatible with the US constitution.
On Wednesday, he tweeted: “Republicans feel that Social Media Platforms totally silence conservatives voices. We will strongly regulate, or close them down, before we can ever allow this to happen. We saw what they attempted to do, and failed, in 2016. We can’t let a more sophisticated version of that happen again.
“Just like we can’t let large scale Mail-In Ballots take root in our Country. It would be a free for all on cheating, forgery and the theft of Ballots. Whoever cheated the most would win. Likewise, Social Media. Clean up your act, NOW!!!!”
Twitter’s fact-checking notice was posted on a previous Trump tweet that claimed mail-in ballots could allow widespread voter fraud. It immediately led to a presidential eruption accusing the platform of “completely stifling FREE SPEECH”.
Mr Trump has used Twitter to spread baseless claims about voter fraud in the past, notably that thousands of people were bussed into certain states in order to vote for Hillary Clinton in 2016. Ms Clinton won some 2.8 million more votes than Mr Trump in that election, though failed to carry the electoral college.
Mr Trump’s outburst on Wednesday also followed Twitter’s refusal to delete a number of posts in which he accused a television presenter of murder, again without any evidence.
The widower of Lori Klausutis, an employee of former Republican congressman Joe Scarborough who died some two decades ago in an accident, had asked Twitter boss Jack Dorsey to remove the messages because they sullied his wife’s memory.
Mr Dorsey faces growing pressure to crack down on Mr Trump’s inaccurate and abusive messages. Timothy Klausutis, the widower, pointed out in his letter to Mr Dorsey that the president’s tweets plainly went against the platform’s code of conduct.
“I’m asking you to intervene in this instance because the president of the United States has taken something that does not belong him – the memory of my dead wife – and perverted it for perceived political gain,” Mr Klausutis wrote.
Mr Scarborough and his wife Mika Brzezinski, who jointly present a morning talk show on MSNBC, used to be friends with Mr Trump but they have since fallen out.
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