Washington ? Toyota apologized to its customers Monday and said a piece of steel about the size of a postage stamp will fix the gas pedal problem that led to the recall of millions of cars. Repairs will take about a half-hour and will start in a matter of days, the company said.

Toyota insisted the solution, rolled out six days after it temporarily stopped selling some of its most popular models, had been through rigorous testing and would solve the problem for the life of the car.

After a week in which Toyota drivers said they were worried about the safety of their cars and dealers were frustrated by a lack of information, Toyota said it would work to regain the trust of its customers.

“I know that we have let you down,” Jim Lentz, president of Toyota Motor Sales USA, said in a video address.

The repair involves installing a steel shim a couple of millimeters thick in the pedal assembly, behind the top of the gas pedal, to eliminate the excess friction between two pieces of the accelerator mechanism. In rare cases, Toyota says, that friction can cause the pedal to become stuck in the depressed position.

Toyota said car owners would be notified by mail and told to set up appointments with their dealers. It said cars already on the road would get priority over those on the lot.

The recall covered 4.2 million cars worldwide and 2.3 million in the United States, including some of Toyota’s best-selling models, such as the Camry and Corolla. It has recalled millions more because of floor mats that can catch the gas pedal.