The nation's major banks raised their prime lending rates a full percentage point today to the 20 percent record of last spring, and analysts say the rate will hit new highs before it starts to decline.

Chase Manhattan Bank, the nation's third largest, was the first institution to increase its prime lending rate from 19 percent to 20 percent, but nearly all major banks were quick to follow, including Riggs National Bank in Washington.

David Rockefeller, chairman of the bank, said in an interview that it costs Chase 20 1/2 percent to borrow funds in the open market. "Even with the raise to 20 percent, we're still losing money at the margin," the banker said.

Interst rates have risen sharply in the last month, mainly because the Federal Reserve, the nation's central bank, has been trying to fight inflation by holding down the growth of money and credit in the economy.

A rising complaint among many businessmen and economists is that the Fed's high-interest-rate policy will choke off the economy, drive up unemployment and add to the inflation rate by sharply raising business costs.

"I hope and assume we're close to the top," Rockerfeller said.

Federal Reserve officials have complained that they are getting no help in the anti-inflation fight from Congress or the administration.

There is some evidence that the Federal Reserve's monetary stringency is beginning to dampen inflation psychology in a few markets. Futures prices of many commodities have fallen in recent days, and the price of gold and silver has tumbled, too, as interest rates have risen. Today's prime rate increase also knocked the pins out of the stock market. The Dow Jones average of 30 major industrial stocks fell 17.83 points to 916.21. Three weeks ago, in the exuberance following Ronald Reagan's election, investors pushed the Dow average above 1,000 for a day.

While the economy may be hurting because of record interest rates, the dollar is not. Demand for dollars is extremely strong around the world because investors want to take advantage of high rates here. As a result, the value of the dollar in foreign markets has risen sharply.

Rockefeller said that the prime rate is increasing primarily because costs of borrowing in the open market are increasing. However, he said, loan demand by businesses and others is a factor.

According to William Sullivan, vice president of the Bank of New York, short-term business credit demands jumped $5.8 billion in November. Most of that increase, $5.4 billion, was bank loans. During the last three months, short-term business credit demands climbed $15.3 billion. They declined $655 during the prior three months.

During the summer, however, when interest rates plummeted after hitting record levels in April, businesses returned to the long-term securities markets rather than obtaining their needed funds on a short-term basis.

Rockefeller said that the near collapse of the bond market in recent months has driven companies to their banks for funds those businesses normally would raise by selling bonds or other long-term securities.

Because long-term interest rates have fluctuated widely this year, many normal investors in corporate bonds have shied away from the market. Furthermore, many companies are reluctant to guarantee investors 16 percent interest for 25 to 30 years, preferring to borrow for short periods from their bankers on the belief that short-term and long-term interest rates will come down soon.