Joe Young, of the Insurance Institute for Highway Safety, drives a 2018 Tesla Model 3 at the IIHS-HLDI Vehicle Research Center in Ruckersville, Va., in July. (Amanda Voisard/Reuters)

Federal safety regulators accused Elon Musk of issuing “misleading statements” on his company’s Tesla Model 3 last year, sending a cease-and-desist letter after the chief executive claimed it was safer than other vehicles.

The National Highway Traffic Safety Administration admonished Musk for claiming the vehicle had “the lowest probability” of injury ever tested by the agency in its safety ratings program, according to the document obtained by government and legal transparency group PlainSite. That’s because NHTSA said the mass of a vehicle plays a role in passengers surviving crashes, something that’s not directly comparable between cars of differing sizes, despite the Model 3′s five-star rating.

NHTSA referred the matter to the Federal Trade Commission’s Bureau of Consumer Protection, it said, to determine whether that statements constituted “unfair or deceptive acts or practices.” The documents show NHTSA also subpoenaed information from Tesla on crashes involving its vehicles.

The publication of the letters is the latest in a string of woes for Tesla, which has had a rocky few months after a tweet by Musk last year in which he said he had secured funding to take the company private. After an investigation, the Securities and Exchange Commission and Musk agreed he would pay a $20 million fine and relinquish his company chairmanship. The company’s stock has plunged since hitting its all-time high in 2017, falling from nearly $390 to close at $233.42 Wednesday.

Regulators and industry executives have also criticized Musk for his bold predictions on launching a vehicle capable of “full self-driving” as soon as this year, followed by a robotaxi fleet next year, The Washington Post has reported. Those people say that the move to launch the largely unproved and unregulated technology could prove detrimental to the overall industry’s attempts to put self-driving cars on the road.

Tesla has faced lawsuits over its Autopilot technology, which has been active in at least three fatal crashes in the United States. And Consumer Reports said in May that Tesla was showing “what not to do on the path toward self-driving cars” with its Navigate on Autopilot feature, which it said was “far less competent” than a human driver.

In 2017, Tesla launched its mass-market Model 3 electric car, which starts at an online price of less than $40,000. The car has proved a popular choice among consumers, helping boost the company to record deliveries last quarter. The Model 3 — along with Tesla’s luxury models — has disrupted the larger automotive industry, which is still working to catch up with its own fully electric vehicles.

Tesla’s Model 3 earned a five-star safety rating from NHTSA in every category, the highest designation available, according to Tesla. The Model 3 also earned a five-star safety rating in Europe’s NCAP safety assessment.

Still, “frontal crash test data cannot determine whether a Model 3 would fare better in a real world frontal collision with, for instance, a significantly heavier SUV,” NHTSA said in its letter. Heavier vehicles typically offer passengers a higher chance of surviving a crash and avoiding injury. “To say that Tesla’s midsize sedan has a lower probability of injury than, say a larger SUV could be interpreted as misunderstanding safety data, an intention to mislead the public, or both."

In response to the allegations in the NHTSA letter, Tesla pointed to previous statements defending its use of the language in question and claiming it arose from NHTSA’s own statements.

“Tesla’s blog statements are entirely based on actual test results and NHTSA’s own calculations for determining relative risk of injury and probability of injury,” wrote Alan Prescott, Tesla’s deputy general counsel, in excerpts of his response letter provided by Tesla. “Based on the foregoing, we do not see a reason to discontinue use of our safety blog or these statements as long as no other vehicle surpasses the Model 3 Long Range RWD’s Vehicle Safety Score and overall probability of injury.”

The NHTSA letter flagged a Tesla blog post titled “Model 3 achieves the lowest probability of injury of any vehicle ever tested by NHTSA,” which remains on its website.

The FTC declined to comment on whether it had opened an investigation or reached a resolution on the matter. NHTSA said that it is committed to rigorous oversight of the industry.

NHTSA’s subpoenas appeared to include requests for information on Tesla crashes in multiple locations — including in Delray Beach, Fla., and Mountain View, Calif.

Walter Huang, a 38-year-old Apple engineer, died after a fiery wreck while driving his Tesla Model X SUV on Autopilot in Mountain View in March 2018, authorities have said. Jeremy Banner, 50, was killed while Autopilot was active when his Model 3 collided with a tractor-trailer in Delray Beach, according to authorities.

The crashes have raised questions over the safety of Tesla’s Autopilot driver-assistance system, which keeps cars within their lanes and performs steering functions, among other features.