The Supreme Court handed the Biden administration a major practical victory on Wednesday, rejecting a Republican challenge that sought to prevent the government from contacting social media platforms to combat what it said was misinformation.

The court ruled that the states and users who had challenged those interactions had not suffered the sort of direct injury that gave them standing to sue.

The decision, by a 6-to-3 vote, left for another day fundamental questions about what limits the First Amendment imposes on the government’s power to influence the technology companies that are the main gatekeepers of information in the internet era.

The case arose from a barrage of communications from administration officials urging platforms to take down posts on topics like the coronavirus vaccine and claims of election fraud. The attorneys general of Missouri and Louisiana, both Republicans, sued, along with three doctors, the owner of a right-wing website that frequently traffics in conspiracy theories and an activist concerned that Facebook had suppressed her posts on the supposed side effects of the coronavirus vaccine.

“The plaintiffs, without any concrete link between their injuries and the defendants’ conduct, ask us to conduct a review of the yearslong communications between dozens of federal officials, across different agencies, with different social media platforms, about different topics,” Justice Amy Coney Barrett wrote for the majority. “This court’s standing doctrine prevents us from exercising such general legal oversight of the other branches of government.”

Justice Samuel A. Alito Jr., joined by Justices Clarence Thomas and Neil M. Gorsuch, dissented.

“For months,” Justice Alito wrote, “high-ranking government officials placed unrelenting pressure on Facebook to suppress Americans’ free speech. Because the court unjustifiably refuses to address this serious threat to the First Amendment, I respectfully dissent.”

The White House welcomed the ruling. “The Supreme Court’s decision is the right one, and it helps ensure the Biden administration can continue our important work with technology companies to protect the safety and security of the American people,” Karine Jean-Pierre, the White House press secretary, said in a statement.

Andrew Bailey, Missouri’s attorney general, said he would continue to try “to build the wall of separation between tech and state.”

“The record is clear: The deep state pressured and coerced social media companies to take down truthful speech simply because it was conservative,” he said in a statement. “Today’s ruling does not dispute that.”

In sidestepping the First Amendment issues in the case, Justice Alito wrote in his dissent, the court had damaged free expression.

“If the lower courts’ assessment of the voluminous record is correct,” he wrote, “this is one of the most important free speech cases to reach this court in years.”

The plaintiffs said that many of the government’s contacts with the social media companies violated the First Amendment; Justice Barrett did not address that argument. But in a notably sharp footnote, she criticized Judge Terry A. Doughty of the Federal District Court for the Western District of Louisiana, who had entered an injunction barring further contacts to address what he said could be “the most massive attack against free speech in United States’ history.”

Justice Barrett wrote critically of Judge Doughty’s “factual findings, many of which unfortunately appear to be clearly erroneous.” Among her examples was a supposed “censorship request” from the administration cited in the judge’s opinion.

“The record it cites says nothing about ‘censorship requests,’” Justice Barrett wrote. “Rather, in response to a White House official asking Twitter to remove an impersonation account of President Biden’s granddaughter, Twitter told the official about a portal that he could use to flag similar issues.”

In dissent, Justice Alito appeared prepared to accept Judge Doughty’s findings, along with their implications.

“Our country’s response to the Covid-19 pandemic was and remains a matter of enormous medical, social, political, geopolitical, and economic importance, and our dedication to a free marketplace of ideas demands that dissenting views on such matters be allowed,” he wrote. “I assume that a fair portion of what social media users had to say about Covid-19 and the pandemic was of little lasting value. Some was undoubtedly untrue or misleading, and some may have been downright dangerous. But we now know that valuable speech was also suppressed.”

He elaborated on that last point in a footnote about the debate over the origin of the virus, reciting evidence that it had leaked from a laboratory. That theory, long embraced by many conservatives who contend that China has evaded responsibility for the pandemic, is now generally acknowledged to be plausible if unproven.

Judge Doughty, who was appointed by President Donald J. Trump, issued a 10-part injunction that prohibited countless 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.”

A unanimous three-judge panel of the U.S. Court of Appeals for the Fifth Circuit, in New Orleans, narrowed the injunction, but not by much.

The panel, in an unsigned opinion, said that administration officials had become excessively entangled with the platforms or used threats to spur them to act. The panel entered an injunction forbidding many officials to coerce or significantly encourage social media companies to remove content protected by 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.

Justice Barrett wrote that the plaintiffs had failed to overcome at least two daunting hurdles in their attempt to establish what was required to show standing: that the government had caused their injuries and that they faced a prospect of future injury.

The first problem, she said, was that the social media companies were independent actors with a demonstrated commitment to addressing misinformation before and apart from the government’s encouragement.

Second, she said, whatever may have happened in the past, particularly in the midst of the pandemic, a plaintiff seeking an injunction must demonstrate a real threat of future injury.

Chief Justice John G. Roberts Jr. and Justices Sonia Sotomayor, Elena Kagan, Brett M. Kavanaugh and Ketanji Brown Jackson joined the majority opinion.

In dissent, Justice Alito focused on the experience of Jill Hines, a health care activist, who helped direct Health Freedom Louisiana, a group that opposed mask and vaccine mandates.

“Hines showed that, when she sued, Facebook was censoring her Covid-related posts and groups,” Justice Alito wrote. “And because the White House prompted Facebook to amend its censorship policies, Hines’s censorship was, at least in part, caused by the White House and could be redressed by an injunction against the continuation of that conduct.”

In May, the court unanimously ruled in favor of the National Rifle Association in a case that raised similar issues. In that case, N.R.A. v. Vullo, the justices said that the group could pursue a First Amendment claim against a New York State official who had encouraged companies to stop doing business with it.

That decision, coupled with the one in the case on Wednesday, Murthy v. Missouri, No. 23-411, sent a disturbing message, Justice Alito wrote.

“What the officials did in this case was more subtle than the ham-handed censorship found to be unconstitutional in Vullo, but it was no less coercive,” he wrote. “And because of the perpetrators’ high positions, it was even more dangerous.”

He added: “Officials who read today’s decision together with Vullo will get the message. If a coercive campaign is carried out with enough sophistication, it may get by. That is not a message this court should send.”