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.