The autonomous vehicle industry has promoted its cars with a promise of increased safety— fewer drunken drivers, texting drivers and other human error that can end in crashes. But on Monday, a self-driving car from Uber Technologies Inc. became the first of its kind to fatally strike a pedestrian.

Soon after the crash in Tempe, Arizona, Uber tweeted that “our hearts go out to the victim’s family” and suspended vehicle testing in multiple cities. The San Francisco-based company was not immediately available for further comment.