Consumer prices rose 0.6 percent last month, a sharp slowdown from the large increases of May and June, the Labor Department reported yesterday.

The good news on the inflation front was somewhat offset, however, by a sharp drop in the stock market and evidence of a continued deep depression in auto sales.

The Dow Jones Industrial Average, after rising more than 100 points in the previous week, dropped 16.27 points yesterday on the second largest trading day in the history of the New York Stock Exchange. The Dow closed at 874.90, and volume on the exchange was 121.65 million shares.

American auto makers reported sales of 131,956 cars domestically in the Aug. 11-20 period, 35 percent below the mid-August figure a year ago, leaving the industry mired in its worst slump in 21 years.

The July increase in the Consumer Price Index, which works out to a 7.3 percent annual rate, was considerably less than the back-to-back 1 percent rises in May and June. The Bureau of Labor Statistics said the prices of fruits and vegetables fell sharply and the rising cost of home ownership and gasoline moderated. The Consumer Price Index for July was 292.2.

The Reagan administration was quick to take credit for the drop in the rate of inflation.

"All in all it is now apparent that this administration, with the cooperation of the Federal Reserve, has achieved considerable progress in reducing the underlying rate of inflation," White House spokesman Larry Speakes said. He said if Congress cooperates with the president in holding down spending, "the specter of runaway inflation will soon be behind us."

But the same policies that have led to a sharp slowdown in the rate of inflation -- even with the hefty May and June jumps, the Consumer Price Index has risen at an annual rate of 5.4 percent during the first seven months of the year -- also have triggered the worst recession in the postwar period.

The unemployment rate is 9.8 percent, the highest level since 1941, companies are operating well below capacity, and bankruptcies are rising at a record rate.

In recent weeks, however, the high interest rates that have plagued the economy have come down sharply. Some key short-term rates have fallen five percentage points in the last two months, and long-term rates, such as the interest charged on mortgages, have begun to edge down as well.

Jerry Jasinowski, chief economist for the National Association of Manufacturers, said the slowing in the inflation rate, coupled with the drop in interest rates and the "strong performance of the stock market gives me confidence that the recovery is finally getting under way."

In another report, the Labor Department said that average weekly earnings of workers rose 0.2 percent in July, when inflation is factored in. In June earnings fell 1.4 percent and were down 1.4 percent for the 12 months ending in July.

Robert G. Ortner, chief economist for the Commerce Department, said the overall price report was "not bad," and that he expected the rate of inflation for the full year would be 6 percent or less. Ortner said only one area of the Consumer Price Index seems impervious to the general decline in inflation: medical care costs. Month in and month out, the price of medical care rises about 1 percent, as it did again in July.

Economists are confident that prices will rise more slowly in coming months because of the leveling off of gasoline and home ownership costs. Energy prices are expected to stay stable for the foreseeable future.

Most economists felt the big cost-of-living increases in May and June were aberrations, caused by low oil inventories (which have grown), the temporary agreement among oil producers to restrict output and stop price-cutting, and a temporary, unexplained increase in housing prices.

The Labor Department said housing costs rose 0.5 percent last month, compared with 1 percent in June and 1.4 percent in May. Gasoline prices rose 2 percent, following a 5.4 percent increase in June. Still, the Labor Department said, gasoline prices are 7.7 percent below their peak of March, 1981.

Grocery store prices fell 0.4 percent, after adjustment for seasonal variation, mainly because of a 2.8 percent fall in fruit and vegetable prices. Restaurant prices rose 0.6 percent.

Clothing prices rose 0.5 percent last month, after a 0.1 percent increase in June.