SAN FRANCISCO — A group of investors in the ride-hailing company Uber has formed an alliance to push Benchmark, a major shareholder, off the company’s board of directors, the latest escalation of a public feud in Uber’s top ranks.

In a letter sent to Benchmark on Friday, Shervin Pishevar, a venture capitalist at Sherpa Capital, demanded that the firm surrender its seat on the Uber board and sell its shares in the company to outside investors, according to a copy of the letter obtained by The New York Times.

The request came a day after Benchmark filed a lawsuit against Travis Kalanick, Uber’s former chief executive, accusing him of fraud, breach of contract and breach of fiduciary duty. Mr. Kalanick resigned as chief executive in June in the face of a shareholder coup led by Benchmark.

“We do not feel it was either prudent or necessary from the standpoint of shareholder value, to hold the company hostage to a public relations disaster by demanding Mr. Kalanick’s resignation, along with other concessions, on a few hours’ notice and within weeks of a personal tragedy, under threat of public scandal,” said the letter, which was signed by Mr. Pishevar and claimed to represent other shareholders.