General Motors Co. Chief Executive Mary Barra took to video to rebut charges its vehicles are unsafe, allegations that have surfaced in the wake of the auto maker’s recall of 1.6 million vehicles with faulty ignition switches.

“The simple answer is yes” the cars are safe to drive, Ms. Barra said of recalled Chevrolet, Saturn and other vehicles. “GM engineers have done extensive analysis to make sure if only you have the key or only the key on a ring, the vehicle is safe to drive. In fact, when they…