Late last month, Cruise paused all its public testing operations while it investigated the incident that led to the recall.

The update will alter the way the car responds after an impact is detected. In an infamous San Francisco accident, the vehicle had incorrectly determined that it was struck on the side rather than hitting something in the front.

Cruise did not detail exactly what the software update changes, only that it "remedies the issue described in this notice."

The cars can be returned to service once the updates are completed, Cruise said in its report to NHTSA. Cruise doesn't sell its self-driving vehicles so all the cars are owned by either Cruise or GM, which produces the heavily modified Chevrolet Bolt electric vehicles.

The company will perform the software updates itself.