Judge Doughty had prohibited officials from “threatening, pressuring or coercing social media companies in any manner to remove, delete, suppress or reduce posted content of postings containing protected free speech.”

The panel wrote that “those terms could also capture otherwise legal speech.” The panel’s revised injunction said officials “shall take no actions, formal or informal, directly or indirectly, to coerce or significantly encourage social media companies to remove, delete, suppress or reduce, including through altering their algorithms, posted social media content containing protected free speech.”

Summarizing its conclusion, the panel wrote: “Ultimately, we find the district court did not err in determining that several officials — namely the White House, the surgeon general, the C.D.C. and the F.B.I. — likely coerced or significantly encouraged social media platforms to moderate content, rendering those decisions state actions. In doing so, the officials likely violated the First Amendment.”

Two members of the panel, Judges Edith B. Clement and Jennifer W. Elrod, were appointed by President George W. Bush. The third, Judge Don R. Willett, was appointed by Mr. Trump.