WASHINGTON — Toyota apologized to its customers yesterday 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.

In Hawai'i, Servco Pacific Inc. said all of its Toyota dealers will be extending service hours to accommodate the expected surge in requests for repairs. The service department at Servco's largest Toyota dealership, in Māpunapuna, will be open 24 hours a day to accommodate customer demand, said Mark Fukunaga, Servco chairman and chief executive officer.

"We want to assure our customers that the Toyota cars they drive are safe and reliable, so we will act quickly," he said.

Fukunaga noted that there have been no confirmed reports of accidents in Hawai'i involving sticking gas pedals.

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.

Jeffrey Liker, a University of Michigan engineering professor who has studied Toyota for 25 years, said he believed the fix would work, citing the automaker's reputation for careful testing and engineering.

"They are under the gun. They aren't playing any games," he 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 today and tomorrow.

Earl Stewart, who owns a Toyota dealership in North Palm Beach, Fla., and had been critical of delays in getting repair parts to dealers, said he was happy with the fix. He said he was reassured that it had been tested by independent engineers, not just Toyota's.

"You never say you're absolutely sure about anything, but I feel that this is probably the answer," he said.

The National Highway Traffic Safety Administration said it had "no reason to challenge this remedy." Transportation Secretary Ray LaHood said last week the government had urged Toyota to issue the recall and suspend production and told reporters yesterday that Toyota had "done the right thing."

NHTSA continues to investigate the issue and was looking into the possibility of electrical problems, said a Transportation Department official.