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.

Michael Anderson, with Fred Anderson Toyota, at 9101 Glenwood Ave. in Raleigh, said Monday that the dealership has people working 24 hours a day to get the repair work done.

"We're setting up new processes and making sure we have the right people in place. We are extending service hours and bringing in a third shift of technicians to make sure we are able to do the work ... as quickly as possible,” Anderson said.

Toyota would not give an estimated cost for the repair work. It estimated repairing all the recalled cars would take months. It said some dealers were planning to stay open around the clock to make the repairs once parts arrive. Parts were expected to begin arriving late Tuesday and Wednesday.

The National Highway Traffic Safety Administration continues to investigate the issue and was looking into the possibility of electrical problems, said a Transportation Department official. The official, who spoke on condition of anonymity to discuss an ongoing investigation, said electromagnetic interference might cause the throttle control systems in the Toyota vehicles to malfunction but NHTSA had not seen evidence to support that yet.