Mr Levandowski likened the Volvos' abilities to those of Tesla cars that have the Autopilot feature which allows them to steer without a person touching the wheel and to brake and accelerate without a person touching the pedals.
He queried why the Tesla vehicles on California's roads did not need a permit if Uber's cars did.
The mayor of San Francisco has sided with the state and a consumer advocacy group has suggested California should do more than force Uber to stop.
"We believe their activity is a criminal offence under the motor vehicle code, punishable with up to six months in jail," John Simpson of the Consumer Watchdog group said.
"(Uber) CEO Travis Kalanick should be arrested immediately."
But in a sign of the level of interest in the technology, the mayor of Beverly Hills has voiced his support for Uber testing without a state permit.