The prime lending rate today resumed its seemingly inexorable climb back to the record levels it reached last spring.

Chase Manhattan Bank touched off the latest increase this morning, raising the interest it charges its best corporate customers for a short-term loan to 18 1/2 percent from 17 3/4 percent. Within hours nearly every major bank in the nation followed Chase's lead.

And in Washington, Riggs National Bank said its prime will go from 17 3/4 percent to 18 1/2 percent Wednesday.

Last April the prime rate hit a record 20 percent, then declined rapidly in the spring and early summer, dropping to 11 percent in July. But in August, the prime rate began to climb again along with interest rates in the open markets.

A spokesman for Chase Manhattan, the nation's third-largest bank, said the bank increased its prime lending rate "to a more appropriate level to cover the cost of our funds, which have continued to rise in recent days and are in excess of 18 percent." If Chase maintained a 17 3/4 percent prime rate, the bank would be lending money at a loss to corporate customers, he said.

Banks raise a sizable portion of the funds they lend to customers by borrowing themselves in the open market, issuing short-term securities called certificates of deposit. To borrow funds for three months, banks have to pay interest rates in excess of 17 1/2 percent. Because they cannot lend all of the funds they raise (the Federal Reserve requires banks to set aside a portion as "reserves"), the real cost to the bank is higher than 17 1/2 percent.

The prime lending rate -- probably the most carefully watched bank interest charge because other business lending charges are built on it -- has skyrocketed from 14 1/4 percent in less than a month, in large part because the Federal Reserve Board has been trying to cut down on the availability of credit in the economy in an attempt to fight inflation.

As a result of the stringent Federal Reserve policy, interest rates in the open market have risen sharply, raising fears that the economy will head into a new downturn as high interest costs choke off both business and consumer borrowing.

ALBERT C. Cox, chief economist for Merrill Lynch & Co., the biggest brokerage firm in the country, predicted today that the nation will slide back into recession for the first half of 1981 due in no small measure to the pinch of rising rates.

For example, automobile manufacturers, who already have lost billions of dollars in 1980, are encountering sales problems with their newly introduced models bacause many potential buyers cannot get bank financing for new cars or because they cannot afford to pay off loans at the current level of rates.

Treasury Secretary G. William Miller, who before the presidential election was castigating banks for not lowering interest charges, today told the Senate Finance Committee that interest rates likely will "stay relatively high until there is a change in inflationary expectations." He said he is concerned that the rates will kill the economic recovery and said he cannot predict when there might be a lowering of inflationary expectations because such a change would depend upon policies adopted by the incoming Reagan administration.

The Federal Reserve, the nation's central bank and architect of monetary policy, today gave analysts no reason to expect a sudden decline in interest rates. When the key open market interest rate, the so-called federal funds rate, declined to 17 percent late this morning, the Federal Reserve took steps to drain lendable funds from the banking system. "The Fed seemed to be saying that it doesn't want the rate to go below 17 percent," said one New York analyst.

On Monday, the Fed tolerated a federal funds rate well above 18 percent without taking steps to supply credit. fThe federal funds rate is the interest banks charge each other for overnight loans of excess reserves. Until a little over a year ago, the central bank used to try to control the level of money and credit in the economy using a target federal funds rate. Since Oct 6, 1979, however, the central bank has said its primary focus is on the money supply directly and that it will permit interest rates to fluctuate more widely than it had in the past.