By Omar Abdel-Baqui 

Tesla Inc. Chief Executive Elon Musk said the electric-vehicle maker hasn't signed a deal with Hertz Global Holdings Inc. yet, which appeared to contradict a Hertz announcement late last month that the company was ordering 100,000 Teslas.

"I'd like to emphasize that no contract has been signed yet," Mr. Musk said in a tweet late Monday. "Tesla has far more demand than production, therefore we will only sell cars to Hertz for the same margin as to consumers. Hertz deal has zero effect on our economics," he said.

Representatives for Tesla weren't immediately available for comment.

In late October, Hertz said it ordered 100,000 Teslas to be delivered to the rental-car company by the end of next year, a bulk purchase that promised to expose more mainstream drivers to Tesla's technology.

After Mr. Musk's tweet, a Hertz spokeswoman Tuesday morning appeared to stand by its earlier announcement. She also said deliveries of Tesla have already started.

"As we announced last week, Hertz has made an initial order of 100,000 Tesla electric vehicles and is investing in new EV charging infrastructure across the company's global operations," the Hertz spokeswoman said. "We are seeing very strong early demand for Teslas in our rental fleet, which reflects market demand for Tesla vehicles," she said.

In the Hertz announcement last month, it said it was partnering with NFL quarterback Tom Brady to promote Tesla's EV campaign. The company's online press release included a video interview with NFL quarterback Tom Brady discussing his experiences with EVs

Tesla didn't put out a press release when Hertz announced the deal.

Mr. Musk at the time tweeted: "Strange that moved valuation, as Tesla is very much a production ramp problem, not a demand problem." He added in a separate tweet: "To be clear, cars sold to Hertz have no discount. Same price as to consumers."

Tesla shares dropped 3.7% premarket. The stock has soared in recent days following the Hertz announcement, topping $1 trillion in market value. Mr. Musk's personal net worth also exceeded $300 billion in the days following the announcement and was recently $335 billion, according to the Bloomberg Billionaires Index.

Hertz shares have risen 38% since the Tesla deal was announced on Oct. 25. Hertz's shares have been traded over the counter since the company was delisted in the summer of 2020.

Hertz had said that Tesla Model 3s would be available for customers to rent in some markets beginning in early November. It said electric vehicles would comprise more than 20% of its global fleet including the Tesla order.

Rental-car companies including Hertz have struggled to meet demand as post-vaccination travel ramped up and as a semiconductor shortage stalled vehicle production.

Write to Omar Abdel-Baqui at omar.abdel-baqui@wsj.com