Sales of cars built in the United States rose 8.7 percent in early September from their level for the same period last year, but the auto industry's rebate-inspired boom apparently is fading, according to reports released today.

Automakers said they sold 152,381 U.S.-built cars between Sept. 1 and Sept. 10, up from 140,155 in the same period last year.

But the seasonally adjusted annual rate of sales declined slightly to 7.6 million from 8.1 million last month.

Rebates and other price-cutting sales promotions had boosted sales in August to an unexpectedly high 23.7 percent above their levels for August 1980 and had trimmed dealer inventories to more manageable levels. But Arvid Jouppi, an independent Detroit-based auto industry analyst, said the improvement was not impressive.

"Sales are still poor," Jouppi said. He said interest rates 80 percent higher than year-ago levels still are restricting new-car sales.

While calling current sales poor, Jouppi said he believes the introduction of 1982 models next month and accompanying deals on leftover 1981 models will spur a major sales surge in October.

"They call this a feast-or-famine business," Jouppi said. "We've had 50 months of feast followed by 30 months of famine. I think the famine will be over at the end of this month."

General Motors Corp. said it sold 94,505 cars in early September, up 6 percent from 89,134 last year. Ford Motor Co., which began offering rebates during the period, said its sales climbed 26.6 percent to 33,081 from 26,133 last year.

Chrysler Corp. reported sales of 18,321 domestic cars, up 2 percent from 17,961. Volkswagen of America, the only domestic automaker that isn't offering rebates or other special sales incentives, said it sold 2,974 U.S.-built Rabbit sedans, down 9.2 percent from 3,275.

American Motors Corp. sales were estimated at 3,500, representing a decline of 4.2 percent from 3,652 last year. AMC and foreign automakers report sales only at the end of each month.

The trade journal Automotive News said the sales promotions helped automakers reduce car inventories to almost normal levels during August. The publication said automakers had a 64-day supply of cars Sept. 1, down from a record 87 1/2-day supply Aug. 1. A 60-day supply is considered ideal.

Each of the automakers except VW had some kind of sales incentive program in effect during the period. GM extended its offer of 13.8 percent interest rates on new-car loans through Sept. 23, and Chrysler did the same with its $300 to $1,000 rebates.

Ford extended its program of dealer incentives and added rebates on certain models to the pot. Like GM and Chrysler, Ford's incentive plan runs through Sept. 23.

AMC is offering $100 to $1,000 dealer incentives on certain models and $500 customer rebates on its Concord models.

So far this year, U.S. automakers have sold 4.56 million cars.