TOKYO, Japan (CNN) -- Toyota has added the brake system of a Lexus hybrid vehicle to a growing list of problems with various models, the company said Friday.
The company said it was checking the brakes on one of the Lexus hybrids, the HS250h, as well as a Japanese model called the Sai -- because they use the same system as that used on the 2010 Toyota Prius.
Toyota (TM) has announced no recall of these vehicles, however, and said it has not received any complaints about the brakes from consumers.
But the U.S. National Highway Traffic Safety Administration (NHTSA) announced Thursday it is opening a formal investigation into problems with the Prius, Toyota's fourth-best selling model in the United States and the best-selling model in Japan.
The company has admitted to a software glitch that is causing problems with its braking. It said it is looking further at the best way to repair the problem.
On Thursday, Ford (F, Fortune 500) announced that it was changing the software in the braking system for its Fusion and Mercury Milan hybrids to correct an occasional glitch in the old software. Ford said no injuries had been reported involving the problem.
David Champion, the head of auto testing at Consumer Reports, said the Fusion/Milan's issue seemed less serious than that of the Prius.
The NHTSA investigation involves only 2010 model year Prius hybrids, which went on sale in the middle of last year. There are only 37,000 of those vehicles on the road, according to the agency.
The Prius, which is built in Japan, is not one of the eight models that was affected by two recent recalls -- covering several million vehicles -- to fix problems with sticking gas pedals. All of those models were built at North American plants.
NHTSA said its Office of Defects investigation has received 124 reports from consumers about problems with the Prius brakes, including four reports that involved crashes and two that resulted in injuries. No fatalities have been reported. Investigators have spoken with consumers and conducted preliminary field work.
Late Wednesday, U.S. Transportation Secretary Ray LaHood spoke with Toyota president, Akio Toyoda, who reassured him that Toyota takes U.S. safety concerns seriously and puts safety at the top of the company's priorities, according to NHTSA's statement.
Toyota had only limited comment on the probe.
"We have heard about NHTSA's intention to begin an investigation. Toyota will cooperate fully with NHTSA's investigation," the company said in a statement.
Even if the solution ends up being a relatively simple and inexpensive software adjustment, the Prius braking problems come at a bad time for Toyota, which has seen its prized reputation for quality and safety badly damaged by the recalls and the news attention given to them.
The company has estimated that the problem with the gas pedals will cost it about 100,000 sales this year, and $2 billion in repair costs and lost revenue.
Other experts say the problem could be more long-lasting if consumers who once trusted the Toyota brand decide to shop elsewhere.
Toyota said Thursday that the Prius problem is a "disconnect" in the vehicle's complex anti-lock brake system that causes less than a one-second lag before the brakes start to work. At 60 mph, though, a vehicle will have traveled nearly another 90 feet before the brakes begin to take hold.
The company also said it changed the braking system software in January for vehicles built since then. But it has yet to determine how to fix the brakes of vehicles already on the road.
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