Tesla shares fell in early trading on Tuesday after founder Elon Musk cast doubt on a deal to supply Hertz with rental cars.

The Hertz announcement last week of an agreement for Tesla to supply the car rental firm with 100,000 of its electric autos helped push Musk's company to a $1 trillion market valuation alongside tech titans like Amazon, Microsoft, Google and Apple.

But Musk on Monday said no agreement had been finalized.

"If any of this is based on Hertz, I'd like to emphasize that no contract has been signed yet," Musk tweeted in response to a chart showing Tesla's share price ascending.

"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."

In a statement, Hertz, which emerged from a bankruptcy re-organization earlier this year, re-iterated it had "made an initial order of 100,000 Tesla electric vehicles and is investing in new EV charging infrastructure across the company's global operations.

"Deliveries of the Teslas already have started. We are seeing very strong early demand for Teslas in our rental fleet, which reflects market demand for Tesla vehicles," the rental car firm said.

Around 1430 GMT, Tesla shares were one percent lower, recouping some of their losses after opening around two percent lower. Meanwhile, Hertz was 11.9 percent higher.

Separately, the US National Highway Traffic Safety Administration on Tuesday announced the recall of nearly 12,000 Tesla cars due to errors with their communication software.

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© 2021 AFP