Tesla and its CEO, Elon Musk, repeatedly described the company's Model 3 sedan as the safest car ever tested by US regulators — claims that earned Musk a cease-and-desist letter last October.

The transparency group PlainSite on Tuesday published a letter from the National Highway Traffic Safety Administration taking issue with the claim that "there is no safer car in the world than a Tesla."

It did not dispute that the Model 3 deserved its 5-star rating after NHTSA tests. But the letter said it was wrong to describe the Model 3 as safer than other 5-star vehicles.

Musk had tweeted a link to a Tesla blog post with the caption "The physics of how Tesla achieved best safety of any cars ever tested."

In a response to the safety agency, a Tesla lawyer denied that the company had misled anybody. Tesla has not responded to the letters becoming public.

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Tesla CEO Elon Musk earned a harsh rebuke from the US road-safety regulator for describing the Tesla Model 3 sedan as the safest car in the world, according to newly published documents.

Musk was sent a cease-and-desist letter by the National Highway Traffic Safety Administration in October, according to the transparency group PlainSite, which on Tuesday published the letter among a cache of correspondence between Tesla and the regulator.

PlainSite said it acquired the documents from public-records requests under the Freedom of Information Act.

The letter, dated October 17, said Tesla had made "a number of misleading statements" about the safety of the Model 3. Musk also distributed the claims on social media.

A Tesla Model 3. Matthew DeBord/BI

The safety claim was linked to the 5-star rating the safety agency awarded the Model 3 in September.

NHTSA ratings are calculated on the basis of numerical tests, many of which saw the Model 3 record the highest result.

But according to the agency, this does not equate to a car being "safer" than others with the 5-star label. It highlighted an October 7 Tesla blog post in which the company said the Model 3 "achieves the lowest probability of injury of any vehicle ever tested by NHTSA."

The agency told Musk that this and other claims had "misled customers."

Musk shared a link to the blog post on his personal Twitter account. It quoted Tesla saying "There is no safer car in the world than a Tesla" and added a line of his own that said "The physics of how Tesla achieved best safety of any cars ever tested."

Two days after the Tesla blog post was published, the NHTSA issued a veiled response to Tesla. It did not name the company but wrote there was "no 'safest' vehicle among those vehicles achieving 5-star ratings."

Read more: My Lyft driver taught me so much about his Tesla Model 3, I feel way more compelled to buy one. Here are the 10 most interesting features I discovered.

In the letter addressed to Musk, the agency said Tesla did not follow its guidelines correctly. It said it would ask the Federal Trade Commission to investigate any "unfair or deceptive" statements.

The PlainSite documents include a response from Al Prescott, one of Tesla's lawyers, in which he denies that Tesla misled customers.

Musk before he unveiled the Model Y at Tesla's design studio on March 14. AP Photo/Jae C. Hong

"Tesla has provided consumers with fair and objective information," he wrote in the letter, dated October 31.

Jonathan Morrison, a lawyer for the agency, had said: "This is not the first time that Tesla has disregarded the guidelines in a manner that may lead to consumer confusion and give Tesla an unfair market advantage."

The agency has taken issue with Tesla's safety claims before.

In 2013, Tesla said its Model S achieved an NHTSA safety rating of 5.4 stars. The agency responded by saying five stars was the maximum, Bloomberg reported.

The PlainSite documents also include subpoenas for information on several Tesla crashes.

Read more: 'Aladdin' star says a defect in his Tesla Model 3 led to his car wreck, and it comes from a problem area the company has known about for years

One of these related to the high-profile March 1 death of Jeremy Beren Banner, a 50-year-old who died when his Tesla crashed into a tractor-trailer while using Tesla's autonomous Autopilot feature.

Another subpoena related to a Model 3 that crashed January 25 in San Ramon, California.

Tesla referred Business Insider to the October 31 letter it wrote to the NHTSA in response to the cease-and-desist when asked for comment.

The letter said: