Elon Musk and Tesla have escalated their war of words with US regulators, accusing them of an "endless investigation" to curb the tycoon's right to free speech.

The allegations surfaced in a lawyer's letter to US District Judge Alison Nathan, who presided over a 2018 Securities and Exchange Commission (SEC) settlement stemming from Musk's tweet about a potential buyout of Tesla.

Alex Spiro wrote: "The SEC seems to be targeting Mr Musk and Tesla for unrelenting investigation largely because Mr Musk remains an outspoken critic of the government; the SEC's outsized efforts seem calculated to chill his exercise of First Amendment rights."

The letter was written against a backdrop of legal trouble for Tesla.

Musk dances onstage during an event for Tesla Model 3 cars

It disclosed earlier this month that it had received a subpoena from the SEC about its compliance with the 2018 settlement.

Then, Musk was found to have fallen foul of market rules when he tweeted that he had "funding secured" to potentially take his electric car company private at $420 per share.

In reality, a buyout was not close.

Tesla and Musk settled by agreeing to each pay $20m in civil fines and to let Tesla lawyers vet some of Musk's communications in advance, including tweets that could affect Tesla's stock price.

Musk also gave up Tesla's chairmanship.

The latest subpoena was issued late last year after Musk polled his Twitter followers on whether he should sell 10% of his Tesla stake, triggering a sell-off.

The Tesla factory in Fremont, California

The lawyer's letter on behalf of Musk and Tesla was filed eight days after California's department of fair employment and housing sued Tesla over allegations by black workers that it tolerated racial discrimination at its Fremont, California, plant.

Tesla, which described that lawsuit as "misguided", is also trying to reduce or throw out a $137m jury award to a black former elevator operator who was allegedly subjected to a hostile work environment at the factory.

Another body, the National Highway Traffic Safety Administration, said on Thursday that it had opened an investigation into Tesla Model 3 and Model Y vehicles after receiving complaints about unexpected braking tied to its Autopilot system.