The Federal Reserve Board yesterday lowered from 11 1/2 to 11 percent the interest it charges on loans to member banks, an indication that the Fed supports the sharp decline in short term interest rates that has occurred during the last month. Less than two weeks ago it cut the rate from 12 to 11 1/2 percent

Moments before it announced the cut in the key rate, the central bank announced that the nation's basic money supply--the most important target of Federal Reserve policy--fell $800 million in the week ended July 22. The decline will permit the Fed to ease monetary policy, relaxing upward pressure on interest rates.

In another development, the Commerce Department announced yesterday that the government's leading economic indicators showed a zero rate of change in June, while sales of new single-family houses fell 14 percent, to a seasonally adjusted annual rate of 343,000 units, nearly wiping out a 17 percent increase in May.

In response to the discount-rate cut and the decline in the money supply, interest rates fell further in the open market where companies and financial institutions buy and sell funds. William Sullivan, vice-president of the Bank of New York, said short-term interest rates fell as much as three-eighths of a percentage point moments after the announcements were made, while the price of long-term government bonds jumped $10 for each $1,000 of face value. When bond prices go up, interest rates go down.

The Federal Reserve's monetary policy, which has spawned sky-high interest rates for most of the last three years, has been blamed for pushing the economy into one of its worst recessions in history. But tight Fed policy seems to have succeeded in helping reduce the rate of inflation from more than 12 percent two years ago to about 6 percent at the current rate.

The recent decline in short-term rates is in large part attributable to the Fed, analysts said. The key open market interest rate the Fed controls, the federal funds rate, has dropped from 14 percent a month ago to about 11 percent today. Other interest rates, such as the rate on certificates of deposit banks issue to raise money, have fallen from about 15 percent to less than 12 percent.

In response, major banks have cut their key prime rate--the rate on which most business borrowing charges are based--from 16 1/2 percent to 15 1/2 percent and yesterday Pittsburgh's Mellon Bank trimmed its prime to 15 percent. More banks are expected to follow suit next week, and even further reductions in the prime are anticipated.

Even with recent rate declines, however, interest rates remain high by historical standards and with prices coming down, many companies are financially exhausted, unable to continue to pass along the high interest charges in price increases. Many analysts expect the high rate of bankruptcies to worsen in coming months, despite rate declines.

Commerce Secretary Malcolm Baldrige said the zero rate of change in the leading economic indicators means initial economic recovery "is likely to be moderate."

The Commerce Department said the composite measurement of economic indicators was stationary in June after increases of 1.4 percent for April and 0.9 percent for May that followed an 11-month string of declines.

Baldrige, who had predicted that June figures would show clear evidence of an economic turnaround, did not abandon his forecast for better times but said it would come later. "I believe we will see clearer signs of economic recovery during the third quarter," he said.

In a separate report, the Commerce Department said the average price of a new house in June was a record $88,100, with a 9.1 month supply of houses on the market unsold.

Last month's sales were the third-slowest on record in government statistics going back to 1963. And they continued what has been--despite scattered gains--a dreary year for the housing industry.

Michael Sumichrast, chief economist for the National Association of Home Builders, said he now expects this year's sales to be well under last year's 436,000, the total that now stands as the worst year in the two decades the government has kept such figures.

"We don't expect any improvement in sales the rest of the year," was his bleak summation.

The blame, as usual, was laid to high interest rates, which make it expensive for builders to finance new house construction and almost impossible for many Americans to pay for home loans to buy the houses that do get built.

The composite index of indicators, designed to forecast periods when the economy reaches a turning point, remained at 127.9 in June compared to a 1967 base of 100, the department said.

Three of the 10 available indicators gave evidence the economy was improving. They were the level of initial unemployment claims, the pace of deliveries and raw materials prices.

But six others reflected more deterioration in the economy. Stock prices contributed most of the decline and inflation-adjusted new orders, orders for business equipment, building permits, changes in liquid assets and money supply were also negative.

The indicator for the length of the average workweek was unchanged.