Word of the remedy came as the French automaker Peugeot said it was recalling cars it builds with Toyota at a plant the companies operate together in the Czech Republic, widening a recall that has already affected cars in the United States, Canada, and China and throughout Europe.

Toyota presented a plan for repairing the potentially sticky pedals to the National Highway Traffic Safety Administration, a senior official at the Transportation Department said. The official spoke on condition of anonymity.

The safety agency is not required to approve remedies but can reject them if it thinks they will not sufficiently address defects. The agency did not reject the remedy, the Transportation official said.

Toyota officials phoned dealers Saturday to say that a remedy was ready.

“We got the call this morning,” said Peter Blackstock, the owner of Victory Toyota and Lexus Monterey Peninsula in Seaside, Calif. “The parts are on their way.”

A Toyota spokesman, Mike Michels, said the company planned an announcement next week and would send letters to owners, but he cautioned it could take several weeks for notices to arrive. Toyota wants owners to wait for the letters before they take their cars to dealerships for repairs, he said.

Mr. Blackstock said he expected that dealers would be sent replacement accelerator pedals, which are produced for Toyota by CTS, a parts supplier based in Elkhart, Ind.

Separately on Saturday, the traffic safety agency said it had opened an investigation into the manufacture of the accelerator pedals.

Last week, Toyota said it would temporary stop production and sales of eight models — as well as sales of the Pontiac Vibe, which Toyota makes on behalf of General Motors — at plants throughout the United States and Canada. The plants are scheduled to be closed for a week beginning on Monday.

Toyota did not stop production or sales at plants in Europe because it said it had already devised and implemented a remedy there.

The recall for accelerator pedals involves 4.1 million cars in the United States, Europe and elsewhere. Toyota has also recalled another 5.4 million cars in the United States whose accelerator pedals could get stuck on floor mats. Worldwide, the recalls affect more than 9.5 million vehicles.

The recalls have given a black eye to Toyota, which grew to become the world’s largest automaker, and the second largest in the United States, based on a reputation for building high-quality vehicles.

On Friday, Toyota’s chief executive, Akio Toyoda, apologized for the problem but said consumers should feel confident driving the company’s cars.

Toyota’s competitors have tried to capitalize on the company’s troubles by offering trade-in deals to Toyota owners. But it is still unclear what effect the recalls might have on Toyota’s sales in the United States.

Edmunds.com, a Web site that provides car-buying advice, forecast that Toyota’s market share for January would fall to a four-year low. But AutoTrader.com, which tracks consumers’ shopping habits, said consideration of Toyota brands had actually risen over the last few days.

Mr. Blackstock, the California dealer, said he hoped repairs could be completed quickly. He said he did not think the recalls would have a lasting effect on his business, or that of Toyota.

“If this is the worst thing that happens to us this year, it should be a pretty good year,” Mr. Blackstock said.