(Adds statement from Hertz)

Nov 2 (Reuters) - Tesla Inc's top boss Elon Musk said the company had not signed a contract with Hertz, more than a week after the car rental firm announced a massive deal with the electric carmaker.

Tesla's shares fell 4% in early trading on Tuesday, after a steep jump following the news of the biggest-ever order - 100,000 electric cars for Hertz - on Oct. 25, which helped Tesla breach $1 trillion in market capitalization.

Musk tweeted late Monday, "If any of this is based on Hertz, I'd like to emphasize that no contract has been signed yet."

"Hertz deal has zero effect on our economics."

Tesla did not immediately respond to a request for comment.

However, Hertz said in a statement that the deliveries of the Teslas had already started.

"We are seeing very strong early demand for Teslas in our rental fleet, which reflects market demand for Tesla vehicles."

Hertz's interim Chief Executive Officer Mark Fields had told Reuters last week the order will primarily include Model 3 vehicles. Considering Tesla's cheapest Model 3 sedan starts at about $44,000, the order could be worth about $4.4 billion, if the entire order were for the mass-market sedan.

"Tesla has far more demand than production, therefore we will only sell cars to Hertz for the same margin as to consumers," Musk said.

Separately, Tesla is recalling nearly 12,000 U.S. vehicles sold since 2017 because a communication error may cause a false forward-collision warning or unexpected activation of the automatic emergency braking system, the National Highway Traffic Safety Administration said. (Reporting by Eva Mathews in Bengaluru; Editing by Shinjini Ganguli and Shailesh Kuber)