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"No, I think that would be up to the individual's insurance," Musk said. "If it is something endemic to our design, certainly we would take our responsibility for that."
Tesla declined to elaborate further on the statement.
Musk made the remark when asked by a journalist if Tesla would take a similar approach as Volvo has said it will when it comes to its driverless cars getting in accidents.
Volvo has said it will accept full liability for any automobile accident that involves one of its self-driving cars.
Musk compared taking responsibility for a self-driving car crash to getting stuck in an elevator.
"Point of views on autonomous cars are much like being stuck in an elevator in a building. Does the Otis [Elevator Company] take responsibility for all elevators around the world, no they don't."
Tesla's Autopilot is still under investigation by the National Highway Traffic Safety Administration. Tesla's Autopilot was activated when a driver died in a fatal crash in May.
A tractor trailer was making a left turn in front of the Tesla when the accident occurred. The Tesla passed under the trailer before driving off the road, smashing through two fences, and ultimately crashing into a power pole.
Tesla wrote in a blog post at the time that the Autopilot system did not notice "the white side of the tractor trailer against a brightly lit sky, so the brake was not applied."
Tesla
A Tesla also got into a crash in China when driving in Autopilot mode, the company confirmed, according to Reuters. There were no injuries from the accident.
Musk criticized media coverage of Tesla Autopilot crashes.
"One thing I should mention that is, frankly, it's been quite disturbing to me, is the degree of media coverage of Autopilot crashes," he said. "[It] is basically almost none relative to the paucity of media coverage of the 1.2 million people that die every year in manual crashes."
"It is something that I think does not reflect well upon the media. It really doesn't," he continued.