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Tesla Chairman and Chief Executive Elon Musk has rubbished claims made on Thursday from an alleged employee of the car company's California branch that workers had been underpaid, overworked and often suffered preventable injuries.

Jose Moran alleged in a Medium post that "excessive mandatory overtime," frequent injuries, and below average hourly pay were hallmarks of the San Francisco Fremont plant in which all of Tesla's cars are manufactured.

NICHOLAS KAMM | AFP | Getty Images

"Frankly, I find this attack to be morally outrageous. Tesla is the last car company left in California, because costs are so high," Musk said in a direct message on Twitter via Gizmodo.

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Moran also accused the car company of attempting to silence its own employees in an effort to prevent them from forming a workers union.

"Many of us have been talking about unionizing, and have reached out to the United Auto Workers (UAW) for support... But at the same time, management actions are feeding workers' fears about speaking out," Moran said in the Medium post.

"Recently, every worker was required to sign a confidentiality policy that threatens consequences if we exercise our right to speak out about wages and working conditions," he added.

Musk rejected all the claims made in the blog post in his direct message to Gizmodo. In addition, he also questioned the authenticity of the worker making the claims against Tesla.

"Our understanding is that this guy was paid by the UAW to join Tesla and agitate for a union. He doesn't really work for us, he works for the UAW," Musk suggested.

"The UAW killed NUMMI and abandoned the workers at our Fremont plant in 2010. They have no leg to stand on," he concluded.

CNBC contacted Tesla on Friday, but a spokesperson was not available for comment.