Most of the nation's major banks raised their prime lending rates today from 19 percent to 19 1/2 percent as short-term and long-term interest rates continued to rise.

The increase in rates drove stock prices down sharply. The Dow Jones industrial average closed down 12.96 points at 963.44. The average is about 60 points lower than it was two weeks ago.

The increase in the prime lending rate -- the key interest charge on which banks base most of their other business-loan charges -- was the second in as many Mondays and reflects rising interest rates in the open market where banks buy many of the funds they then lend to customers.

Chase Manhattan Bank, the nation's third-largest, was the first to boost the key lending rate, but Chase was followed rapidly by most other major banks. Riggs National Bank, Washington's largest, said it would raise its prime rate to 19 1/2 percent on Tuesday.

The steady increase in the prime rate during the last month reflects in the main a tight-money policy on the part of the Federal Reserve Board, the nation's central bank. The bank is trying to hold down the growth of the money supply (essentially cash and checking accounts) by stifling the availability of credit in the economy. It does that by trying to keep funds away from banks. When money becomes less available, its price -- the interest rate -- rises.

Treasury Secretary Donald T. Regan, who recently changed his prediction of sharply falling interest rates, commented in a speech in washington yesterday that "there is no way to get inflation down with interest rates coming down at the same time."

William Sullivan, vice president of the Bank of New York, said interest rates climbed steadily in all areas of the money markets today, a development he called "surprising".

Unlike last week, when the Fed took steps on both Thursday and Friday to drain lendable funds from banks, the central bank was inactive today, and the key interest rate it controls, the federal funds rate, traded quietly in the range of 18 1/4 percent, Sullivan said. Furthermore, the money supply, which had been growing sharply in recent weeks, declined $3.6 billion last week. Shortly after the Red reported the decline, interest rates fell in late trading.

Sullivan said the rise in rates -- which also spells a decline in prices for long-term securities such as bonds -- was steady all day. He said part of the increase might be attributable to a recurrent rumor that Federal Reserve Chairman Paul A. Volcker was about to resign.

When asked about the rumor, a spokesman for Volcker said "there is absolutely no truth to it".

Today's increase in the prime lending rate is due to interest rate increases that occurred last week and the week before. Banks try to peg their key lending rate to the costs they must incur in raising funds.

Most analysts expect that the Federal Reserve will keep money tight for several more weeks until it gets the growth of the money supply back on a lower path, although last week's decline may permit the central bank to stop tightening interest rates until it gets a better reading of the money-supply situation.

Burton M. Siegel, chief of research at the brokerage firm Drexel Burnham Lambert In., said he anticipates that it will be another month before interest rates stop climbing. "How high will they go? No one knows," he said.