When the environmental group Greenpeace lost a nearly $670 million verdict this month over its role in oil pipeline protests, a quarter-billion dollars of the damages were awarded not for the actual demonstrations, but for defaming the pipeline’s owner.

The costly verdict has raised alarm among activist organizations as well as some First Amendment experts, who said the lawsuit and damage awards could deter free speech far beyond the environmental movement.

The verdict “will send a chill down the spine of any nonprofit who wants to get involved in any political protest,” said David D. Cole, a professor at Georgetown Law and former national legal director of the American Civil Liberties Union. “If you’re the Sierra Club, or the N.A.A.C.P., or the N.R.A., or an anti-abortion group, you’re going to be very worried.”

The lawsuit, filed by Energy Transfer in 2019, accused Greenpeace of masterminding an “unlawful and violent scheme” to harm the company’s finances, employees and infrastructure and to block the construction of the Dakota Access Pipeline. Greenpeace countered that it had promoted peaceful protest and had played only a minor role in the demonstrations, which were led by the Standing Rock Sioux Tribe over concerns about its ancestral land and water supply.

A key part of Energy Transfer’s case relied on defamation claims. For example, the jury found that Greenpeace defamed the company by saying it had “damaged at least 380 sacred and cultural sites” during pipeline work, the first of nine statements found defamatory.

Greenpeace called Energy Transfer’s lawsuit an attempt to muzzle the company’s critics. “This case should alarm everyone, no matter their political inclinations,” said Sushma Raman, interim executive director of Greenpeace USA. “We should all be concerned about the future of the First Amendment.”

Greenpeace has said it will appeal to the Supreme Court in North Dakota, the state where the trial was held. Free-speech issues are widely expected to figure prominently in that filing.

But Greenpeace was not the only party invoking the First Amendment.

Upon leaving the courtroom, the lead lawyer for Energy Transfer, Trey Cox of Gibson, Dunn & Crutcher, called the verdict “a powerful affirmation” of the First Amendment. “Peaceful protest is an inherent American right,” he said. “However, violent and destructive protest is unlawful and unacceptable.”

Vicki Granado, a spokeswoman for Energy Transfer, described the verdict as “a win for all law-abiding Americans who understand the difference between the right to free speech and breaking the law.”

The clashing comments shine a light on a central tension in the debate: Where do you draw the line between peaceful protest and unlawful activity?

“If people are engaged in non-expressive conduct, like vandalism, like impeding roadways such that cars and passers-by can’t use those roadways, the First Amendment is not going to protect that,” said JT Morris, a senior supervising attorney at the Foundation for Individual Rights and Expression, a nonprofit that defends free speech across the ideological spectrum. “But peaceful protest, criticism of companies on matters of public concern, those are all protected.”

The verdict landed in the midst of a larger debate over the limits of free speech. President Trump has accused news outlets of defaming him, and he has been found liable for defamation himself. His administration has targeted law firms he perceives as enemies, as well as international students deemed too critical of Israel or of U.S. foreign policy. Conservatives have accused social media platforms of suppressing free speech and have vowed to stop what they call online censorship.

“There’s nothing in this particular political climate that’s shocking anymore,” said Jack Weinberg, who in the 1960s was a prominent free-speech activist and later worked for Greenpeace. (He’s also known for the phrase “Don’t trust anyone over 30,” although that’s not exactly how he said it.) “But it’s wrong,” he said of the verdict, “and it will have profound consequences.”

There has long been a high bar for defamation lawsuits in the United States.

The First Amendment protects free speech and the right to protest, and a landmark 1964 Supreme Court decision, New York Times v. Sullivan, strengthened those protections. To prevail in a defamation suit, a public figure must prove that the statement was false and was made with “actual malice,” meaning knowledge that the statement was false, or reckless disregard for its veracity.

Carl W. Tobias, a professor at the University of Richmond School of Law, said that ruling intentionally raised the bar to win a defamation suit. “It’s extreme,” he said. “It’s meant to be.”

Eugene Volokh, a senior fellow at the Hoover Institute at Stanford University, pointed to the history of that famous case. It concerned a 1960 ad in The Times that described police actions against civil rights demonstrators in Alabama as “an unprecedented wave of terror.”

A police official sued the paper and won. But the Supreme Court overturned the verdict. The court ruled that protecting such speech was necessary, even if it contained errors, in order to ensure robust public debate.

In a Greenpeace appeal, Mr. Volokh said, the evidence demonstrating whether Greenpeace’s statements were true or false would be crucial in evaluating the verdict, as would the question of whether Greenpeace’s statements were constitutionally protected expressions of opinion.

Other issues that loom: What was permitted to be entered into evidence in the first place, and whether the instructions to the jury were sufficient. Then, he said, if the statements are found to be clearly false, is there enough evidence to show that Greenpeace engaged in “reckless falsehood, acts of so-called actual malice?”

Any award for defamation chills free speech, Mr. Volokh added, whether against Greenpeace or against the Infowars host Alex Jones, who was found liable for more than $1 billion over his false statements about the murder of children at the Sandy Hook school shooting.

In the Greenpeace case, the nine statements found by the jury to be defamatory referred to Energy Transfer and its subsidiary Dakota Access. One statement said that Dakota Access personnel had “deliberately desecrated burial grounds.” Another said that protesters had been met with “extreme violence, such as the use of water cannons, pepper spray, concussion grenades, Tasers, LRADs (Long Range Acoustic Devices) and dogs, from local and national law enforcement, and Energy Transfer partners and their private security.”

Other statements were more general: “For months, the Standing Rock Sioux have been resisting the construction of a pipeline through their tribal land and waters that would carry oil from North Dakota’s fracking fields to Illinois.”

The protests unfolded over months, from mid-2016 to early 2017, attracting tens of thousands of people from around the world, and were widely documented by news crews and on social media.

Janet Alkire, chairwoman of the Standing Rock Sioux Tribe, argued that Greenpeace’s statements were true and not defamatory. “Energy Transfer’s false and self-serving narrative that Greenpeace manipulated Standing Rock into protesting DAPL is patronizing and disrespectful to our people,” she said in a statement, using an abbreviation for the Dakota Access Pipeline.

She said that “scenes of guard dogs menacing tribal members” were publicly available “on the news and on the internet.”

Videos of the incidents in question weren’t shown at the trial. Everett Jack Jr. of the firm Davis, Wright Tremaine, the main lawyer for Greenpeace, declined to discuss why.

The 1,172-mile pipeline, priced at $3.7 billion when announced, has been operating since 2017. It carries crude oil from North Dakota to Illinois.

During the trial, some arguments hinged on whether the pipeline crossed Standing Rock’s land, or how to define tribal land. The pipeline is just outside the borders of the reservation but crosses what the tribe calls unceded land that it had never agreed to give up.

There was also debate about whether tribal burial grounds were harmed during construction. Experts working for the tribe found that was the case, but experts brought in by Energy Transfer did not.

Even if a statement was false, Mr. Cole said, a defendant cannot be held liable if they had a basis for believing it. He also predicted that the penalty would likely be reduced on appeal if not overturned.

Martin Garbus, a veteran First Amendment lawyer, led a delegation of lawyers to North Dakota to observe the trial, who have said that the jury was biased against the defendants and that the trial should have been moved to another county. He expressed concern that an appeal to the U.S. Supreme Court could be used to overturn Times v. Sullivan. He noted that Justice Clarence Thomas has called for the Supreme Court to reconsider that case.

But Mr. Cole, Mr. Tobias and other experts said they did not expect the court to reconsider Times v. Sullivan.

Greenpeace has said previously that the size of the damages could force the organization to shut down its U.S. operations.

The lawsuit named three Greenpeace entities, but it centered on the actions of Greenpeace Inc., based in Washington, which organizes campaigns and protests in the United States and was found liable for more than $400 million.

A second organization, Greenpeace Fund, a fund-raising arm, was found liable for about $130 million. A third group, Greenpeace International, based in Amsterdam, was found liable for the same amount. That group said its only involvement was signing a letter, along with several hundred other signatories, calling on banks to halt loans for the pipeline.

Earlier this year, Greenpeace International filed a countersuit in the Netherlands against Energy Transfer. That lawsuit was brought under a European Union directive designed to fight what are known as SLAPP suits, or strategic lawsuits against public participation — legal actions designed to stifle critics. (State law in North Dakota, where Energy Transfer brought its case against Greenpeace, doesn’t have anti-SLAPP provisions.)

The next hearing in the Netherlands case is in July.