Domestic new-car sales stayed in the fast lane in mid-July, running 38.6 percent better than in the year-ago period.

The increase is based on a seasonally adjusted annual rate, meaning that if U.S. car sales continue at their current pace, domestic automakers could sell 7.7 million cars in 1983. The seasonally adjusted annual rate for mid-July 1982 was 5.6 million cars.

Sales of 7.7 million cars for the full year of 1983 would be 33 percent higher than last year's actual total of 5.8 million--the domestic auto industry's worst sales performance since 1961.

In the period between July 11-20, the automakers sold 206,875 cars, compared with 132,938 in the same period last year. The daily selling rate of 22,986 cars per day was the best for the period since 1979.

General Motors Corp. sold 128,390 cars in the mid-July period, up 45.6 percent from 78,382 last year; Ford Motor Co. sold 43,718, up 26.6 percent from 30,686; Chrysler Corp. sold 26,043, up 26 percent from 18,698; American Motors Corp. sold 4,450 cars, up 60 percent from 2,700; and Volkswagen of America Inc. sold 2,098 cars, down 24.6 percent from 2,472. Honda, which began manufacturing Honda Accords this year in Marysville, Ohio, sold 1,816 of its U.S.-built cars in the period.

The mid-July report--reflecting nine selling days, compared with eight in the 1982 period--marks the sixth consecutive increase in domestic car sales in 60 days. The improvement is coming in all size categories, automakers and industry analysts said yesterday.

"The people coming back into the market are buying a broad range of cars," said Philip E. Benton, Ford Motor Co.'s vice president of sales. "All sizes, from small to luxury, have experienced substantial increases, with mid-size cars showing the largest gains," Benton said of the industry's performance.

"I think they're telling the truth" about the breadth of the sales gains, said David Healy, an auto industry analyst with New York-based Drexel Burnham Lambert.

"The rush towards the bigger cars slowed down in the last two months, and the sale of smaller and mid-size cars began picking up. It could mean that the recovery is broadening," bringing many middle-income buyers back into the market, Healy said. graphics/1&2 photo&chart: The first American Motors Corp. Encore, successor to the popular Alliance, rolls off the production line at Kenosha, Wis., last week.