June 12 (Reuters) - Rocket maker SpaceX and its CEO Elon Musk were sued on Wednesday by eight engineers who say they were illegally fired for raising concerns about alleged sexual harassment and discrimination against women, their lawyers said.

The engineers - four women and four men - claim Musk ordered their firing in 2022 after they circulated a letter calling the billionaire a "distraction and embarrassment" and urging executives to disavow sexually charged comments he had made on social media. The lawsuit was filed in state court in Los Angeles, according to the lawyers, Anne Shaver and Laurie Burgess.

The lawsuit says Musk's conduct fostered a "pervasively sexist culture" at SpaceX where female engineers were routinely subjected to harassment and sexist comments and their concerns about workplace culture were ignored.

"These actions ... had the foreseeable and actual result of offending, causing distress, and intruding upon Plaintiffs’ well-being so as to disrupt their emotional tranquility in the workplace," the plaintiffs said in the lawsuit.

SpaceX did not immediately respond to a request for comment.

SpaceX has denied wrongdoing, saying the 2022 letter was disruptive and the workers were properly fired for violating company policies.

Paige Holland-Thielen, one of the plaintiffs, said in a statement provided by her lawyers that Wednesday's lawsuit is an attempt to hold SpaceX leadership accountable and spur changes in workplace policies.

"We hope that this lawsuit encourages our colleagues to stay strong and to keep fighting for a better workplace," she said.

The eight engineers are already the focus of a U.S. National Labor Relations Board case claiming that their firings violated their rights under U.S. labor law to advocate for better working conditions.

SpaceX filed a lawsuit claiming that the labor board's in-house enforcement proceedings violate the U.S. Constitution. A U.S. appeals court last month paused the NLRB case while it considers SpaceX's bid to block it from moving forward pending the outcome of the company's lawsuit.

Wednesday's lawsuit accuses SpaceX and Musk of retaliation and wrongful termination in violation of California law, and further accuses the company of sexual harassment and sex discrimination.

The plaintiffs are seeking unspecified compensatory and punitive damages and an order barring SpaceX from continuing to engage in its allegedly unlawful conduct.

(Reporting by Daniel Wiessner in Albany, New York Editing by Alexia Garamfalvi and Matthew Lewis)