The U.S. auto industry barely had time to bask in the glow of unaccustomed profits in the past quarter before returning to the uphill grind of selling cars in a stagnant auto market.

General Motors Co. was the last of the American firms to report second-quarter earnings, and it led the field with a $515 million profit for the April-June period, a gain of nearly $1 billion from the $412 million loss in the same period a year ago.

Ford Motor Co. reported a $60.2 million second-quarter profit last week, led by a strong recovery by its North American operations, and Chrysler Corp. -- so close to financial oblivion for long -- had an $11.6 million profit, the first black ink in two years. American Motors Co. lost $19.9 million in the second quarter, but that was substantial improvement over the $88.1 million deficit in the second quarter of 1980.

With GM's earnings report yesterday, however, came another announcement, a new sales incentive program designed to save GM buyers an average of $550 per car on all 1981 GM models and the new 1982 J-car line.

The plan is not a rebate, GM said. But it is designed to do the same thing. GM promises buyers of those cars a 13.8 percent interest rate on car loans during August, well below the 16 percent to 18 percent financing rates on typical auto loans today. Depending on the size of the auto loan and the prevailing interest charges, the program should lower a new car owner's monthly financing costs by more than $10 a month.

"We wnat to get people back into our showrooms," said Robert D. Burger, GM's marketing vice president. "We look to this program to help get things moving again."

It wasn't clear whether GM's move would start a new, industry wide incentives-rebate campaign. Ford and Chrysler officials said yesterday they were "studying" the GM move and wouldn't comment. But if GM's interest-rate rollback works, it will bring pressure on the others to follow suit with some new incentives of their own. Currently, only AMC is offering price rebtes on some of its Jeep and Renault models, during July.

The rebate in February and March gave auto sales a powerful boost, raising the industry-wide annual sales rate to 10.3 million units including imports. But with the end of rebates, sales sank steadily, falling to an annual rate of 7.8 million units in June.

GM is plainly disturbed by its backlog of 840,000 unsold new cars in stock -- a 90-day supply. "it's more than we feel comfortable with," Burger said in an interview.

The size of the inventory is compounded because production of the new Chevrolet, Pontiac and Cadillac J-cars is far behind schedule. Only 10,000 Chevrolet Cavalier J-cars are in stock, less than two for each of Chevrolet's 6,000 dealers. When J-car production is rolling dealers will be under more pressure to move cars.

This reality clouds GM's recovery efforts. Second-quarter earnings, equal to $1.72 a share, was the third consecutive quarter of profitable operations and the highest quaterly earnings in two years. However, one-third of GM's earnings last quarter were due to the strength of the dollar in foreign currency transactions, according to industry analysts.

GM's worldwide sales of cars and trucks toatled 2 million units in the quarter, 17 percent more than in the disastrous second quarter of 1980, but still 23 percent below the same period in 1979. Second-quarter sales totaled $18 billion, $4.2 billion above last year's figure, but $1 billion below the record level in 1979.

GM said its hourly payroll costs per worker rose at a much slower rate in the past year than between the second quarters of 1979 and 1980. Its overall payroll was 28.6 percent of sales in the second quarter, compared with 30 1/2 percent in second quarter 1980.

GM is zeoring in on what it feels is consumer resistance to high interest charges, Burger explained.

Chrysler Chairman Lee A. Iacocca also argues that interest rates are crucial. If the prime rate falls to 15 percent this summer, Chrysler would have a "brilliant" last quarter, he said last week. If the prime remains near 20 percent, however, "Look out. There's disater ahead," he added.