Major banks across the nation yesterday raised their key prime lending rates from 10 1/2 percent to 11 percent, the highest level for almost six months and the first nationwide increase in the prime since February 1982.

Stock prices plunged on the news, while the dollar soared to new heights against European currencies, and gold and silver prices declined. The U.S. government also had to pay higher interest on its new debts. Treasury bill rates rose to 9.57 percent for three-month bills and 9.70 for six-month bills at yesterday's weekly auction, the highest yields for almost a year.

The Dow Jones Industrial Average closed down more than 20 points on the day at 1,163, the lowest since April 13. Investors fear that rising interest rates could choke off the economic recovery now under way. Housing is particularly vulnerable to rising interest rates and yesterday the government reported that mortgage rates on new homes jumped to an average of 13.24 percent last month, well above the 12.98 percent recorded in June.

Meanwhile, high U.S. interest rates make the dollar more attractive to foreigners and encourage people to sell other currencies and buy dollars. In recent weeks, the dollar has climbed dramatically against most other currencies, making it harder for American manufacturers to compete with cheaper foreign goods.

The strong market reaction yesterday came despite the fact that an increase in the prime was widely expected. Other interest rates have risen sharply in recent weeks, pushing up the cost of the funds that banks themselves borrow and squeezing their profit margins. Several analysts said that banks had held off from the politically unpopular move of boosting the prime--the rate charged by banks to their key customers--until Congress went home for the summer recess.

The White House said that yesterday's increase brought the prime into line with other market interest rates. Spokesman Larry Speakes said, "We would be hopeful that this does not indicate a trend, that interest rates once again will begin to go down." He added that the administration stood by its forecast of lower interest rates by year-end.

Higher rates "are not good for the recovery," commented presidential economist Martin S. Feldstein. An increase in rates "clearly does weaken further substantial parts of the economy" such as housing, business investment, and industries that compete overseas or with imported goods. Feldstein said that large budget deficits were the main reason for present high interest rates.

The economist added that he expected the economy to continue to grow rapidly in the present quarter, but that the effects of higher rates could be felt in the final quarter of the year. So far, the recovery has been much more vigorous than predicted.

The strength of the recovery is in fact one factor pushing rates up, analysts say. Private credit demands have begun to rise, thus increasing the overall demand for money and the pressure on interest rates.

In addition, the Federal Reserve Board has moved to tighten credit conditions in recent months in an attempt to bring the soaring money supply back under control. Fed Chairman Paul A. Volcker has told Congress that the recovery is strong enough to withstand slight increases in interest rates, but he has called for urgent steps to reduce the deficit.

So far, the Fed has been unable to bring the money supply back into line and some analysts fear that further credit tightening and higher interest rates will be needed to achieve the Fed's money supply growth targets.

Yesterday's prime rate move was led by Citibank of New York, the nation's largest bank, and was quickly followed by other major banks and many smaller ones across the country.

Riggs National Bank in Washington raised its prime rate from 10 1/2 percent to 11 percent, effective today.

However, the half-point increase still does not compensate banks fully for the rise in their cost of funds since May, analysts said yesterday, adding that if market rates do not come down again soon, the prime will likely go up again.