Federal regulators, including the Federal Trade Commission, also could begin to look into complaints of online bias once the executive order is promulgated. A reporting tool the administration set up earlier collected more than 16,000 complaints in a matter of weeks, the draft order says. The FTC, for example, could begin to take enforcement action against companies that limit users' speech in a manner that isn't fully disclosed in their terms of service, or is contrary to the platforms' public claims, on grounds that that constitutes an unfair or deceptive trade practice.

The Justice Department also would convene a working group of state attorneys general to look into complaints under the order, and federal agencies would be directed to review their advertising contracts with companies that engage in speech censorship.

Given the legal and regulatory challenges involved, it would likely be months before any actions proposed in the executive order would take effect on social-media platforms. For now, the initiative casts Mr. Trump as fighting for the rights of his base against a tech-industry establishment that his supporters widely view as biased in favor of liberal positions.

Trump administration officials have been discussing the executive order in various forms since 2018, as the president grew increasingly frustrated with tech companies, people familiar with the discussions said. In recent weeks, those discussions have picked up again. In mid-May, Mr. Trump tweeted that the "Radical Left" was in "total command & control" of Facebook, Instagram, Twitter and Google and said the administration was "working to remedy this illegal situation."

Senate Democratic Leader Chuck Schumer of New York said in a tweet on Thursday: "If President Trump doesn't like Twitter, he can do everyone a favor and stop tweeting."

Deepa Seetharaman and Jeff Horwitz contributed to this article.

Write to John D. McKinnon at john.mckinnon@wsj.com and Rebecca Ballhaus at Rebecca.Ballhaus@wsj.com