Hyundai is adding about 6,100 more Veloster hatchbacks to a recall for sunroofs that can shatter and rain glass onto the driver and passengers.
In December, the automaker announced the recall of 13,500 of its Veloster coupes from the 2012 model year for the same problem.
Hyundai says the panoramic sunroof assembly may have been weakened during installation at the factory.
At least five people have suffered minor injuries when sunroofs in the Velosters shattered, though no crashes have resulted.
In October, the National Highway Traffic Safety Administration launched an investigation into the problem after receiving complaints from consumers.
Consumers have complained of the same problem in vehicles made by Kia, Hyundai's sister company.
Hyundai will notify owners, and dealers will inspect the sunroof's integrity and replace the sunroof glass assembly, as necessary, free of charge. The safety recall will begin in March. Owners may contact Hyundai at (800) 633-5151.