SAN FRANCISCO (CBSLA/AP) — Uber is halting tests on all of its autonomous vehicles in San Francisco and three other U.S. cities after police in a Phoenix suburb say one of Uber’s self-driving vehicles struck and killed a pedestrian.

Police in the city of Tempe said Monday that the vehicle was in autonomous mode with an operator behind the wheel when the woman walking outside of a crosswalk was hit.

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Sgt. Ronald Elcock says in an email that the accident happened overnight but did not say whether it occurred Sunday night or Monday morning.

The woman died of her injuries at a hospital and her name was not made public.

In a statement Monday, Uber said: “Our hearts go out to the victim’s family. We’re fully cooperating with @TempePolice and local authorities as they investigate this incident.”

Dara Khosrowshahi. the company’s CEO, tweeted this statement: Some incredibly sad news out of Arizona. We’re thinking of the victim’s family as we work with local law enforcement to understand what happened.

According to Bloomberg News, in response to the death, Uber suspended driverless testing in Pittsburgh, San Francisco, Toronto and the greater Phoenix area.

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Uber has been testing the self-driving vehicles in Tempe and Phoenix for months. Late last month, California announced new rules that will allow driverless cars to be tested in California for the first time without a person behind a steering wheel.

CBSLA’s Tina Patel spoke to Jamie Court, president of Consumer Watchdog. He doesn’t think that the California DMV should relax their regulations on driverless cars the way Arizona has.

“Until we see what came out of Arizona today and why this person died, we should have a moratorium on all robot car testing in America,” said Court. “Arizona is the Wild Wild West for these robot cars. There’s no sheriff. And this is what happens. You have deaths. So in California, we need to see this as a wakeup call.”

But right now the majority of accidents on the roads are caused by drivers. That’s why some say computers might be the answer.

“I don’t know, do you drive in LA? It’s crazy here. If there was some more safety rules put in, it could actually work better for people in the long run,” said Southern California driver Jane Beal.

Some drivers say as tragic as the death in Arizona is, new technology is always dangerous. Things tend to get safer over time.

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(© Copyright 2018 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)