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.”

In a later decision, the panel added the Cybersecurity and Infrastructure Security Agency and six of its officials and employees.

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.

In their Supreme Court briefs, the two sides agreed that the case was momentous, if for different reasons.

“The implications of the Fifth Circuit’s holdings are startling,” Ms. Prelogar wrote. “The court imposed unprecedented limits on the ability of the president’s closest aides to use the bully pulpit to address matters of public concern, on the F.B.I.’s ability to address threats to the nation’s security, and on the C.D.C.’s ability to relay public-health information at platforms’ request.”