The Tempe Police Department said it was investigating the crash, and has not determined whether the car was at fault. A Volvo XC90 sport utility vehicle equipped with Uber’s sensing technology struck Elaine Herzberg, 49, while it was going 40 miles an hour in a 45-mile-an-hour zone. According to the police, the car, with one safety driver and operating in autonomous mode, did not slow down before impact.

A video shot from the vehicle’s dashboard camera showed the safety driver looking down, away from the road. It also appeared that the driver’s hands were not hovering above the steering wheel, which is what drivers are instructed to do so they can quickly retake control of the car. Ms. Herzberg, pushing a bicycle across the street, appeared in the camera right before she was hit.

“As we develop self-driving technology, safety is our primary concern every step of the way,” said Matt Kallman, an Uber spokesman. “We’re heartbroken by what happened this week, and our cars remain grounded. We continue to assist investigators in any way we can.”

Uber has been testing its self-driving cars in a regulatory vacuum in Arizona. There are few federal rules governing the testing of autonomous cars. Unlike California, where Uber had been testing since spring of 2017, Arizona state officials had taken a hands-off approach to autonomous vehicles and did not require companies to disclose how their cars were performing.

Waymo and Cruise, a self-driving car company owned by GM, reported their “intervention” numbers to California regulators. Uber’s goals in Arizona were mentioned in internal documents — Arizona does not have reporting requirements — and it has not been testing self-driving cars in California long enough to be required to report them.

Uber’s first road tests in its self-driving car effort, code-named Project Roadrunner, were actually in Pittsburgh in September 2016. The Phoenix area was added a year ago, and quickly became the company’s main testing ground, with 400 employees and more than 150 autonomous cars driving local roads because of "favorable regulatory environment, favorable weather conditions,” according to a company document.

When Mr. Khosrowshahi took over as Uber’s chief executive, he had considered shutting down the self-driving car operations, according to two other people familiar with Mr. Khosrowshahi’s thinking.