The new system will be put in all vehicles globally, said Yoshi Inaba, president of Toyota North America Inc., in an interview at the Detroit auto show on Monday. The initiative follows a recall last fall of 3.8 million Toyota and Lexus vehicles in the United States to correct the problem.

Inaba said installation began this month on the Toyota Camry and Lexus ES 350 models, which account for the largest number of models included in the recall.

“We expect to have it standard on all vehicles by the end of the year,” he said.

Several instances of runaway Toyota and Lexus vehicles have been reported in the United States, causing injuries and some deaths. Toyota concluded that those cases were the result of floor mats becoming lodged under accelerator pedals. But the National Highway Traffic Safety Administration has said the floor mats were not necessarily the only cause.

Toyota spokesman Mike Michels says the brake override software system will shift the engine to idle if it detects the driver is attempting to apply the brakes without success.

“If the pedal is stuck, tampered with, no matter what the pedal is doing, the engine will go into idle,” he said.

Toyota did not disclose the cost of installing the brake override system.