Commenting on a video showing part of a speech by Michelle Malkin, who has been criticised for backing white nationalist activists, the president said the websites were involved in an "illegal situation", although he declined to say what that was.
He wrote: "The Radical Left is in total command & control of Facebook, Instagram, Twitter and Google. The Administration is working to remedy this illegal situation. Stay tuned, and send names & events. Thank you Michelle!"
Ms Malkin was dropped by the Young America's Foundation, a conservative youth group, following her defence of Nick Fuentes, who has been accused of being a Holocaust denier and white nationalist.
Mr Trump made his comments on Saturday morning as part of a string of attacks on the media, his predecessor Barack Obama and other political opponents.
Meanwhile the death toll from the coronavirus in the US stood at more than 88,000, with 1.4 million cases.
This is not the first time that the president has threatened social media and technology firms. In June 2019 he said the US government should sue them after complaining that they unfairly suppress his message.
Those comments were made on the same day that Congress heard from Facebook, Google and Twitter about misinformation end extremist content spread online.
Speaking on Fox Business, the president said: "Twitter is just terrible, what they do. They don’t let you get the word out. I’ll tell you what, they should be sued because of what’s happening with the bias."
Mr Trump currently has just under 80 million followers on Twitter and posts prolifically.
In the past he has accused Twitter of deliberately limiting his number of followers.
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