Tesla Inc. has doubled the discounts offered on its Model 3 and Model Y electric vehicles delivered in the U.S. this month, according to its website, fueling concern demand for autos from Elon Musk’s car company may be softening.

“Take delivery of a new Model 3 or Model Y between December 21 and 31, 2022 for a $7,500 credit and 10,000 miles of free Supercharging,” the EV maker says on its website.

The charging credits also apply to the Model S and Model X vehicles, according to the company’s website, but not the $7,500 discount.

Discounts are common in the car business, but the $7,500 Tesla is now offering stands out in this current environment, because the auto industry has largely been able to pull back on such incentive programs in recent years with a continuing car shortage driven largely by supply-chain constraints.

“Manufacturer discounts are up slightly from a month ago, however, they remain historically suppressed,” said Thomas King, president of the data and analytics division at J.D. Power. On average, car companies spent $1,187 per vehicle on such promotions in December, according to the consumer research company, and some Tesla rivals have been raising prices on select models.

Mr. Musk has frequently boasted how Tesla stands apart from traditional car companies by not relying on the kind of marketing tools, such as advertisements or discounting, to goose demand.

Shares in Tesla fell more than 9% in Thursday trading. The stock is down more than 60% this year, falling further than the broader market, driven in part by investor concerns about growing competition in the electric-vehicle market, worries about weakening vehicle demand as the economic outlook deteriorates and chief executive Mr. Musk’s heavy involvement in Twitter Inc., which the billionaire acquired in October in a deal valued at $44 billion. The company’s stock is on track for its biggest ever annual decline.

Tesla lists new Model 3 prices currently starting at roughly $48,000, with Model Ys starting at about $66,000, though list prices can vary based on location and other factors.

Auto makers generally try to avoid offering steep discounts because it can damage profits and a brand’s reputation. Tesla’s brand image has slid in recent months, according to surveys, as the car maker faces regulatory challenges and Mr. Musk has waded further into politics in his bid to turn around Twitter.

Tesla frequently adjusts vehicle pricing as demand in various markets fluctuates, though the company offering discounts is rare. The company also has a record of rushing at the end of the year to put vehicles in customer hands to meet targets.

Tesla has said it would likely fall short of its vehicle delivery target this year of boosting handovers around 50% a year. The company has attributed the lower volume to global supply chain disruptions, a temporary idling of its biggest plant in Shanghai, China, earlier in the year, and ramp up challenges at new factories in Germany and Texas.

Demand for cars has softened more broadly as consumers react to a deteriorating economic outlook and rising interest rates. Global volume recovery is stalling, Bernstein Research said in a recent note.

Mr. Musk has said repeatedly Tesla is production, not demand, constrained.

The $7,500 credit for Model 3 and Model Y vehicles is up from the $3,750 credit that Tesla was offering earlier this month.

The Tesla credits come after President Biden in August signed a legislative package that includes EV tax incentives meant to accelerate the transition to cleaner vehicles.

Earlier this week, however, the Treasury Department delayed plans to release detailed rules around the battery-sourcing requirements that electric vehicles must meet to qualify for up to $7,500 tax credit.

Tesla has been rushing to boost production volume to keep pace with wider adoption of electric vehicles. The auto maker is cranking out more vehicles at existing plants and, Mr. Musk has said, aims to add about 10 to 12 new factories for the company to achieve an objective of making 20 million vehicles around 2030.

Separately, the National Highway Traffic Safety Administration said in a notice that it had added two further Tesla crashes involving the company’s advanced driver assistance feature known as Autopilot to its list of special investigations. The U.S. auto-safety regulator said both incidents occurred this month and caused minor injuries.

Write to Will Feuer at Will.Feuer@wsj.com