The nation's major auto makers today reported a 15.8 percent drop in sales for mid-December, the period just prior to the latest round of cut-rate incentive offers.

The period covered in the latest report, Dec. 11 to 20, was before General Motors Corp. touched off the new round of sales incentives on Dec. 26 to move its bulging inventories of more than 1 million unsold vehicles.

Domestic auto makers had limited incentives in place on selected models during the middle of the month, but they did little to rekindle showroom activity as buyers seemed to wait for lower interest rate offers to come along.

The seven companies, GM, Ford Motor Co., Chrysler Corp., Honda Motor Corp., American Motors Corp., Volkswagen of America and Nissan Motor Manufacturing USA, reported combined sales of 165,132 cars in the United States during the period compared with 196,209 units in the year-ago period.

Today, Ford also extended its discounted-loan program to cover two additional models. The company announced that it will offer 7.9 percent financing on new 1985 and 1986 Ford Escort and Mercury Lynx models equipped with manual transmissions and delivered to retail customers from dealer stocks by Feb. 22.

The recent period's daily selling rate was 18,348 cars compared with 21,801 for the same period last year.

The annual rate for the industry during the period was 6.5 million cars compared with 7.7 million last year. Through Dec. 20, the firms sold 7.97 million cars, up 2.6 percent from the 7.77 million units sold in the comparable 1984 period.

There were nine selling days in this year's and the year-ago period.

On a daily-rate basis, GM's sales were off 17.4 percent, Ford's off 19.7 percent and Chrysler's off 12.4 percent.

Among the smaller companies, AMC's sales for mid-December fell 45.5 percent, while Honda reported a 19.6 percent gain on sales of its U.S.-built models only. Volkswagen's domestically built cars posted a strong 41.7 percent gain for the period, but part of the advance was due to unusually low availability of some U.S.-made models last year.

Nissan began production of its Sentra passenger car in Smyrna, Tenn., in late March.