Chase Manhattan Bank, the nation's third largest, lowered its prime lending rate from 11 3/4 percent to 11 1/2 percent today, the first time that key interest rate has been cut in more than two years.

But most analysts concur with Chase Manhattan's statement that "it would be a mistake to interpret this action necessarily as a signal that interest rates have peaked."

The Chase cut in the rate it charges its best corporate customers for a short-term loan takes effect Wednesday. Chase was followed by several other smaller banks in St. Louis and Los Angeles.

Theodore H. t/ung, an economist with Continental Illinois Bank & Trust Co. in Chicago, called the prime rate reduction a "respite," but said that short-term rates will again resume their upward climb in the near future.

Tung said the general reduction in short-term rates in recent weeks has been triggered by extremely low demand for loans on the part of corporations.

These interest rate reductions have occurred despite continued tight monetary policy on the part of the Federal Reserve Board.

The Fed has not changed its monetary posture since a sever tightening last November as part of President Carter's multi-pronged effort to prop up the then-sagging dollar.

The key Federal Reserve target interest rate, the so-called federal funds rate, has remained at or near 10 percent since mid-Novermber. That rate was about 6 3/4 percent last spring.

The low demand for loans on the part of businesses is due to several factors:

Businesses usually need to borrow less in the first few weeks after Christmas.

The economy was much stronger during the last three months of 1978 than nearly all economists anticipated, and corporate profits were very high. That means companies have a lot of cash in their treasuries and do not have to go to banks to finance day-to-day activities such as building up inventories.

Many companies, anticipating an economic slowdown, cut back on their inventories, further reducing their needs.

But Tung said, during the next several months, as companies realize the economy is strong, they again will begin to borrow to build up their stocks.

Furthermore, if the news on the inflation front continues to be as bad as many economists anticipate, the Federal Reserve Board may find it necessary to tighten further its monetary policy, which in turn would raise interest rates.

The first signal that a cut in the prime rate was in the offing came Monday when many major banks reduced the interest they charge brokerage houses for loans that are backed by stocks. The so-called broker loan rate was cut to 11 percent from 11 1/2 percent.

The prime rate. along with most interest rates, has been on a steady upward climb since early 1977, when the rate was 6 1/4 percent. The prime rate rose seven times in 1977 and 15 times last year.

Many economists, such as Henry Kaufman, chief economist for the investment banking firm Salomon Brothers, expect the prime rate will rise to 13 percent or higher this year. The previous peak prime rate was 12 percent during the severe credit crunch of 1974.

Yet some economists, admittedly in the minority, think the Federal Reserve already has tightened monetary policy too much. The money supply -- currency in circulation and checking accounts -- reversed itself in recent months, contracting in November and December after surging in the first 10 months of 1978.

These monetarist economists think the abrupt change in the growth of the money supply could trigger a recession, which in turn would further reduce business demands for loans.