The NHTSA said it would open an investigation into whether a safety defect had caused fires in the undercarriages of two Tesla Model S cars after they struck road debris. A Tesla Motors Model S electric vehicle is seen in Tokyo. (Tomohiro Ohsumi/Bloomberg)

The National Highway Traffic Safety Administration says it will investigate whether a safety defect caused Tesla cars to catch on fire after striking road debris.

The probe, which was announced Tuesday on the agency’s Web site, involves more than 13,000 Tesla Model S electric vehicles.

On Tuesday morning, Tesla chief executive Elon Musk — anxious that fear of fire could dent sales of the cars just as they are starting to gain traction — posted a blog item saying that the company would amend its warranty to cover damage caused by fire “even if due to driver error.” He added that “unless a Model S owner actively tries to destroy the car, they are covered.”

Musk also said the company had asked the NHTSA to investigate the car in order to debunk safety fears, though agency Administrator David Strickland told reporters that he was “not aware of Tesla making a request of the agency to open a formal investigation.”

The investigation will zero in on two accidents in October and November involving Tesla’s Model S, which aced NHTSA crash tests and is being marketed as “the safest car in America.” Two cars, one in Tennessee and one in Washington state, caught fire after they ran over metal objects that punctured the cars’ lithium-ion battery packs, which are mounted underneath the vehicle. A third fire, in Mexico on Oct. 18, followed a high-speed crash. The drivers were not injured.

The fires have stirred concerns among investors, who have driven the lofty price of Tesla stock down considerably. The stock, which started the year selling for less than $34 a share, has been as high as $193.37. At midday Tuesday, the shares had climbed to $127.19 apiece, up about 4.5 percent.

If an investigation were to lead to a recall, it would be a setback for Tesla, which sold about 5,500 cars in the third quarter. Fires in lithium-ion batteries have also been the focus of other investigations, including reviews of General Motors’ Chevy Volt and the Boeing Dreamliner aircraft.

Deutsche Bank analyst Dan Galves said in a note to investors that he “would have found it unusual for NHTSA not to perform a formal investigation given the close timing of the incidents and the sensitivity around fire risk in lithium-ion batteries.” He added that while he believes “the most likely outcome of the investigation is benign, there is no way to know this with certainty.” He said in the roughly 60 days it will take the NHTSA to publish its findings, the investigation would hang over the stock.

Musk responded vigorously in his blog post, which was e-mailed to reporters. He noted that the frequency of fires with the Model S was still much lower than with gasoline-powered cars, claiming “an average of one fire per at least 6,333 cars, compared to the rate for gasoline vehicles of one fire per 1,350 cars.” He added, “You are more likely to be struck by lightning in your lifetime than experience even a non-injurious fire in a Tesla.”

Musk also noted that the Model S battery pack has internal firewalls between its 16 modules, as well as a firewall between the battery pack and passenger compartment.

So far, there have been no reports of anyone killed in a Tesla Model S. Although that record will probably change, Musk conceded, he said that “it is literally impossible for another car to have a better safety track record, as it would have to possess mystical powers of healing.”

Tesla has also posted on its Web site a letter from Juris Shibayama, a Tennessee surgeon who was driving one of the Model S cars that caught fire. In the letter, Shibayama said he was driving 70 mph when he hit “a rusty three-pronged trailer hitch that was sticking up with the ball up in the air.” He said he continued to drive for a couple of minutes until a dashboard monitor instructed him to pull over. He collected his belongings and walked away, he said.

Musk wrote that “we have requested that the National Highway Traffic Safety Administration conduct a full investigation as soon as possible into the fire incidents.” He said that the safety investigation “did not at first seem like a good use of NHTSA’s time compared to the hundreds of gasoline fire deaths per year that warrant their attention,” but that he was concerned about whether “a false perception about the safety of electric cars is allowed to linger.”

In its statement, the NHTSA said its “decision to open any formal investigation is an independent process. In regards to Tesla, the agency notified the automaker of its plans to open a formal investigation and requested their cooperation, which is standard agency practice for all investigations. The automaker agreed to do so.”

In a Twitter post, Musk said that on Friday, Tesla’s vice president of regulatory affairs, Jim Chen, “invited NHTSA senior staff to conduct a review of Model S.”

Tesla has proposed one possible remedy: a software fix that would prevent drivers using the air suspension to lower the vehicle at highway speeds. Drivers can now choose among three ground clearances, from a low of 4.62 inches to a high of 5.75 inches.