Investors, already unnerved by Facebook's plunge, shed Twitter shares. The stock lost 3 percent Thursday, sent lower by a 1 percent additional decline immediately following Trump's comments.
Trump called out a practice commonly called "shadow banning," in which Twitter limits visibility in search results for particular accounts. Trump, following a Vice report about the practice, claimed the company is limiting the reach of "prominent Republicans."
The Vice story claims Republicans such as party chairwoman Ronna McDaniel and Donald Trump Jr.'s spokesperson were among those being de-emphasized in search results.
A spokesperson for Twitter declined to comment on Trump's tweet but told CNBC in an email: "As we have said before, we do not 'shadowban.' We are aware that some accounts are not automatically populating in our search box, and shipping a change to address this. The profiles, Tweets and discussions about these accounts do appear when you search for them. To be clear, our behavioral ranking doesn't make judgments based on political views or the substance of Tweets."
Twitter is a private company and can moderate its platform as it sees fit. Trump did not specify which law he believed Twitter was violating.
Twitter saw similar claims of conservative censorship in the fall, after suspending several extreme-right accounts in an effort to reduce hate speech and threats of violence on the site. Republican lawmakers have also repeatedly accused Facebook of silencing conservative voices, holding several congressional hearings to address the matter in which representatives for Facebook, Twitter and YouTube denied any political bias.
"Our purpose is to serve the conversation, not to make value judgments on personal beliefs," Nick Pickles, Twitter's global lead for public policy strategy, told Congress last week.