Tesla on Monday fired back at a complaint filed last week that its cars could suddenly, and without warning, unintentionally accelerate.

"This petition is completely false and was brought by a Tesla short-seller," the company wrote in a statement on its website.

The company said that it reviews all cases of claimed unintended acceleration and found no errors with its cars. The company claims that its Model S sedan, Model X crossover, and Model 3 sedan have multiple fail-safes to preclude unintended acceleration in its vehicles.

Nonetheless, the company said it has examined the numerous complaints filed with federal safety officials and concluded that its cars did not unintentionally accelerate.

A complaint filed with federal safety officials earlier this month alleged that many owners' tales of unintended acceleration in Teslas could warrant a federal probe. That complaint, filed by Brian Sparks of Berkeley, California, alleges that owners of a 2016 Tesla Model X report unintended acceleration in their cars at 30 times the national average for all cars. The complaint cited 127 consumer complaints, covering 123 unique vehicles, that allegedly led to 110 crashes and 52 injuries.

"I believe Tesla vehicles have a structural flaw which puts their drivers and the public at risk," Sparks wrote in a redacted complaint released by the federal agency last week.

Sparks told CNBC that he is selling short on Tesla's stock, and filed the complaint on behalf of other Tesla owners. It's unclear if Sparks owns a Tesla currently. Sparks claims that up to 500,000 vehicles could be affected by the issue and could be recalled.

Federal regulators likely will announce their initial findings in the next few weeks and decide whether to launch a formal probe or abandon the claims.