DETROIT, JULY 14 -- New car sales in the United States dropped 12.4 percent during the first 10 days of July compared with the same period a year ago, the eight auto companies reported today.

General Motors Corp., Ford Motor Co., Chrysler Corp., American Motors Corp., Volkswagen of America, Honda, Nissan and Toyota sold a total of 165,910 cars during the July 1-10 period, down 12.4 percent from the comparable period in 1986. There were eight selling days in both periods.

Among the Big Three companies, only Ford posted an increase. Ford sold 50,255 cars this year, up 0.8 percent from the early July period a year ago.

GM's sales for the period slipped 22.1 percent to 80,986 this year. Chrysler sold 21,430 cars in the period, off 28 percent.

Among the smaller companies, AMC's sales for July 1-10 dropped 50 percent while VWA's slipped 51.6 percent from year-ago levels. By contrast, Honda's sales were up 235.4 percent and Nissan's shot up 4,927 percent.

For the year to date, the companies have sold 3.8 million cars in the United States, down 12 percent from a year ago.

Once again, Ford was alone among the Big Three in posting a sales gain. Ford has sold 1.07 million cars in the Jan. 1-July 10 period, up 1.6 percent.

GM's year-to-date sales have slumped 22.1 percent to 1.9 million this year. Chrysler has sold 504,379 cars so far this year, down 15.6 percent

AMC's domestic sales this year are down 53 percent while VWA's are off 15.2 percent. Honda's year-to-date sales are up 72.4 percent and Nissan's are up 161.6 percent.

No comparable year-ago figures are available for Toyota because of its recent production startup.