SAN FRANCISCO — An Uber executive accused of stealing driverless car technology from his former employers at Google is exercising his Fifth Amendment right to avoid self-incrimination, according to his lawyers.

The lawyers for Anthony Levandowski, the former head of Google’s self-driving car project who is now leading a similar effort at Uber, said he was broadly asserting his Fifth Amendment rights because there was “potential for criminal action” in the case, according to court transcripts obtained on Thursday.

The legal maneuver adds even more intrigue to the high-profile fight between two of the technology industry’s largest companies, which are squaring off in the race to put driverless cars on the road.

Mr. Levandowski is at the center of a lawsuit between Uber and Waymo, which was spun out from Google to become its own Alphabet subsidiary. Waymo has accused Mr. Levandowski of stealing documents and poaching employees before quitting Google and then colluding with Uber to use that technology to advance driverless car efforts at the ride-hailing service.