WASHINGTON — Ruling that airlines have broad immunity from lawsuits under a post-9/11 security law, the Supreme Court on Monday threw out a $1.4 million defamation judgment awarded to a pilot who was reported by his employer as mentally unstable and potentially armed.

The court was unanimous in holding that a law aimed at encouraging reports of possible security threats to the Transportation Security Administration shields airlines from defamation claims when the reports are substantially true.

“Congress wanted to ensure that air carriers and their employees would not hesitate to provide the TSA with information it needed,” Justice Sonia Sotomayor wrote for the court. Airlines may be held liable only for recklessly false reports, she said.

Applying that reasoning to the case of veteran pilot William Hoeper, the justices voted 6-3 to overturn a Colorado jury’s verdict against Air Wisconsin, Hoeper’s former employer.

The case stems from Hoeper’s final, failed attempt to win airline approval to fly a new aircraft. The session ended with an angry exchange between Hoeper and another employee at a Virginia training facility.

Later that day, Hoeper was a passenger on a United Airlines flight home to Denver that was ordered to return to its gate after Air Wisconsin called TSA with its report of Hoeper as a potential threat.

He was removed from the plane by armed police officers and asked about his gun — properly locked up at home — while his luggage was emptied on the jet bridge.

TSA eventually determined Hoeper was not a threat, but he said he was so embarrassed by the incident that he took a later flight rather than re-board the delayed plane that was still sitting at the gate.

Sotomayor said the airline was basically correct when it reported that Hoeper “may be armed” because he had earlier been certified as a federal flight deck officer who was authorized to carry a gun while on the job to protect passengers and crew. Hoeper was not supposed to carry the weapon when he was not working or in training, and he had appropriately left it home.

She also said that concerns about his mental stability were more or less justified by the anger he showed at the training facility.

Justice Antonin Scalia, joined by Justices Elena Kagan and Clarence Thomas, said the high court should have sent the case back to Colorado courts, possibly for a new trial.

“In short, a jury could find that Hoeper did nothing more than engage in a brief, run-of-the-mill, and arguably justified display of anger that included raising his voice and swearing, but that did not cause anyone, including the person on the receiving end of the outburst, to view him as either irrational or a potential source of violence,” Scalia said.

The case is Air Wisconsin v. Hoeper, 12-315.