(Adds statement from Waymo and background on case)

SAN FRANCISCO, May 18 (Reuters) - Uber will appeal a judge's order rejecting its attempt to arbitrate a high profile trade secrets lawsuit against Alphabet's self-driving Waymo unit, according to a court filing on Thursday.

U.S. District Judge William Alsup last week ruled that Waymo's lawsuit should not be heard in a private forum, and instead should continue to be litigated in San Francisco federal court.

The case, which pits two companies battling to dominate the fast-growing field of self-driving cars, hinges on files that Waymo alleges engineer Anthony Levandowski stole before leaving the company. Waymo claims the information made its way into Uber's Lidar system, a key sensor technology in self-driving cars.

Levandowski left Waymo in January 2016 and started Otto, a self-driving truck startup that Uber bought for $680 million in August. He had until last month run Uber's self-driving car division, before stepping aside from those responsibilities pending the court case.

Alsup also issued an injunction ordering Uber to keep Levandowski away from work involving Lidar, to prevent him and all other employees from using the materials and to return them to Waymo by May 31.

Uber has not yet said in court papers whether it plans to appeal the injunction. An Uber spokesman declined to comment.

A spokesman for Waymo criticized Uber's decision to appeal the order on arbitration.

"Uber's appeal is a blatant attempt to hide their misconduct from the public," the Waymo spokesman said in a statement. (Reporting by Dan Levine and Julia Love; Editing by Sandra Maler)

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