Consumer prices rose at an annual rate of 10.6 percent in August, an improvement over the July rate but still at double-digit levels, as housing costs continued to dominate the government's inflation index.

The increase of 0.8 percent in August marked a sharp decline from the 1.2 percent increase in the consumer price index in July, and resulted from a moderation in price increases for transportation, food and beverages.

"Inflation is still very much a concern of the American economy," Murray Weidenbaum, chairman of the President's Council of Economic Advisers, told economists at a meeting yesterday.

Although inflation is still "painfully high, we are on target to getting a lower rate of inflation this year than last year," said Weidenbaum. Prices have risen at an annualized rate of 9.6 percent so far this year, as reported by the Bureau of Labor Statistics in the CPI.

That is under the administration's forecast of 9.9 percent for 1981, but unless there is a decline from the August rate between now and the end of the year, the 1981 goal won't be met, administration economists acknowledge.

And Jerry Jordan, a member of the CEA, said the August report suggested inflation would come in under 10 percent this year.

"We think we are on course and that inflation will decline further by 1 or 2 percentage points in 1982," he told the congressional Joint Economic Committee yesterday.

The CPI reached 276.5 in August before seasonal adjustment. The base period, which equals 100 on the index, is 1967. Thus a basket of goods costing $100 in 1967 would have cost $276.50 last month.

The Labor Department also reported yesterday that employes' real average weekly earnings, after accounting for inflation, rose one-half percent from July to August, leaving the average for the year down by 0.9 percent. According to this index, average weekly earnings for private, nonfarm workers were $259.88 in August compared with $236.79 a year earlier.

The earnings of a married worker of average income with three dependents rose 0.4 percent after taking out federal income and Social Security taxes. Over the year, real average, after-tax wages have declined 2.7 percent.

High mortgage rates continued to put strong upward pressure on the consumer price index. The housing component has risen 16.2 percent on an annual basis during June, July and August, and last month there were large increases in property taxes, property insurance, rent, and fuel and other utilities as well. The 1.2 percent increase in rental charges on the CPI was the largest in a year.

Administration economists expect continued bad news in the housing sector for several more months, at least. This gloomy outlook is balanced to some extent by the prospect for moderate increases in finished goods. Producer prices for finished goods at the wholesale level rose at a seasonally adjusted annual rate of only 3.6 percent in August, the sixth month this year that the increase was below the 10 percent mark, and this indicates lower consumer prices for finished goods in the next several months.

Medical care costs rose at a high rate for the eighth consecutive month. Hospital rooms rose 2.2 percent in August. Charges by physicians, dentists and other medical professionals rose 0.9 percent, while the cost of medical commodities, including drugs and medical supplies, rose 1.1 percent. The overall increase for medical care was 1.3 percent in August and 15.3 percent at an annual rate for the June-August period.

The food and beverage index rose 0.7 percent in August, just under the increase in July, but well above the rate for the balance of the year. Sizable increases in prices of beef, pork, poultry and fresh fruits and vegetables more than offset declines in egg and milk prices.

Transportation charges increased by 0.6 percent in August, as new-car prices rose moderately and automobile finance charges dropped abruptly. Gasoline prices continued to decline, although by less than in the past four months, the BLS reported.

The average price for all types of gasoline decreased slightly to $1.348 a gallon in August, according to the BLS. Regular gasoline averaged $1.310; unleaded regular, $1.376; and leaded premium, $1.444.