Facebook Inc.’s board of directors threw its support behind Chief Operating Officer Sheryl Sandberg on Wednesday, saying that it was “entirely appropriate” for her to ask if George Soros had shorted the company’s stock after the billionaire investor called the social-media giant a “menace.”

Facebook’s general counsel Colin Stretch sent a letter from the board to Patrick Gaspard, president of Mr. Soros’s Open Society Foundations. Mr. Gaspard has been among those who have criticized or questioned Ms. Sandberg’s handling of the matter.

“To be clear, Ms. Sandberg’s question was entirely appropriate given her role as COO,” Mr. Stretch wrote. “When a well-known and outspoken investor attacks your company publicly, it is fair and appropriate to do this level of diligence.”

The letter was a show of support for Ms. Sandberg, one of the tech industry’s most prominent executives, as investors, regulators, and users renew pressure on both her and the company following a series of management missteps.

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Facebook CEO Mark Zuckerberg is chairman of the board of directors.

Mr. Stretch sent the message at the Facebook board’s request in response to a letter Mr. Gaspard publicized Tuesday. In that communication, Mr. Gaspard said that Ms. Sandberg had misled him during a private phone call on Nov. 15 about her knowledge of company-commissioned opposition research into Mr. Soros by Definers Public Affairs, a consulting firm that Facebook tasked with scrutinizing detractors.

During that call, Ms. Sandberg “assured me that she knew absolutely nothing about these efforts, which included oppo research on George Soros,” Mr. Gaspard wrote in his Dec. 4 letter to the company’s board of directors. “It is now clear from the news that Ms. Sandberg did not speak in good faith.”

On Wednesday, Mr. Stretch disputed Mr. Gaspard’s characterization, saying Ms. Sandberg had been truthful to him about her knowledge of Definers’s work regarding Mr. Soros. Open Society didn’t immediately return a request for comment.

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