Many of the nation's major banks boosted their prime lending rates sharply today from 11 1/2 percent to 12 percent, and the Federal Reserve Board took further steps to tighten its monetary policy.

The Federal Reserve's intervention in the money markets, which took place shortly after the latest round of bank increases began, pushed interest rates up further.

Today's increases in the prime lending rate, the interest banks charge their best corporate customers for a short-term loan, had been anticipated, although the half-point jump was bigger than expected. In the last three weeks the prime lending rate has risen from 11 percent to 12 percent, although it is still well below the record 20 percent it reached in April.

Edward Palmer, chairman of the executive committee at Citibank, said the prime rate rise mainly reflects increasing interest rates in the open market. But he said the bank's decision to increase it a full half-point was influenced by the Labor Department's report today that the unemployment rate fell from 7.8 percent to 7.6 percent and that producer prices jumped 1.5 percent in August.

Inflation and increasing production both put pressure on interest rates.

Chase Manhattan said that loan demand remains moderate and that today's increase in the rate should not be taken as an indication that interest rates are off on another climb. Because banks purchase in the open market most of the funds they lend to customers, rising market rates increase bank loan costs. t

Palmer said he agrees with Chase's assessment, although he thinks there could be some further increases in interest rates before they start declining again.

Despite the decline in unemployment and the increase in hours worked by manufacturing employees, Palmer said that he thinks business will recover slowly from the recession. That will mean reduced loan demand both from banks and in the open market where businesses borrow directly using their own promissory notes, called commercial paper.

Furthermore, Palmer said, inflation should moderate in coming months, too, taking pressure off interest rates. Most of the increase in producer prices was due to food.

The Federal Reserve, however, apparently remains concerned that the money supply (essentially cash and checking deposits) is growing too swiftly and today took steps to drain funds from banks that they otherwise might lend. The action was taken when so-called federal funds were being loaned to 10 1/8 percent. The Fed action pushed the federal funds rate up to 10 5/8 percent, according to Nicholas Marrone of Bank of New York. But the rate settled back to about 10 1/4 percent in later trading, he said.

The Fed's concern about money supply growth seems to be warranted. The central bank reported late today that money grew $500 million in the week ended Aug. 27, from a revised $378.8 billion to $379.3 billion. More importantly, the money supply has been growing at a 13 percent annual rate over the last four weeks, well in excess of the Fed's target range of 7 percent.

Most economists think that if the money supply grows too fast, inflation accelerates. The money supply exploded in the first week of August, jumping a record $9.6 billion. Analysts thought much of that increase might be an aberration caused by flukey technical factors. Instead, most of that increase has stuck.

When the Fed intervenes in the federal funds market -- soaking up bank reserves -- it attempts to reduce the ability of banks to make loans and, therefore, reduce the rate of growth of money. Money is created when a bank makes a loan.

The Federal Reserve also drained reserves from banks on Wednesday. The move stopped a rally in both the money and the bond markets. The federal funds rate, the interest banks charge each other for overnight loans of excess reserves, had declined to 9 1/2 percent Wednesday after three days of steady declines. The Fed can maintain close control over the federal funds rate, a rate off which over short-term rates develop, but the central bank has changed its operating procedures during the last year and has said it will pay less attention to the level of interest rates and more attention to the money supply than it has in the past.

Economists say that although the Fed's moves to tighten money policy may have a short-term impact of raising interest rates, over the long run a reduction in monetary growth should relieve apprehension about inflation and result in a reduction in interest rates.

Besides Citibank and Chase, a number of other major banks raised their prime rates today, including the nation's biggest bank. Bank of America, First National of Chicago and Security Pacific Bank of California.