Major banks boosted their prime lending rates yesterday from 8.75 percent to 9.25 percent, the second half-point jump in a month, bringing the bellwether interest rate to its highest level in a year and a half.

But despite fears in financial markets that the nation is on the edge of a major upswing in rates to be led by the Federal Reserve Board, sources said that Fed chairman Alan Greenspan does not regard yesterday's prime rate increase as a major event.

Contrary to the expectation of some market participants, Greenspan is known to think that yesterday's rise is not the forerunner of another discount rate increase. The Fed last raised the discount rate -- which it charges for loans to financial institutions -- by half a percentage point, to 6 percent, on Sept. 3.

The prime, a benchmark rate banks use for setting charges on many consumer and business loans, could lead to higher rates for adjustable rate mortgages, home equity loans and other borrowings.

The banks' action -- touched off initially by Citicorp and Chase Manhattan Bank -- was triggered by higher short-term money costs incurred by the banks, and reflected a general belief in financial markets that interest rates are headed higher.

It also indicated a growing concern in the banking industry about the impact of recent additions to loan-loss reserves on profitability. Reserves have recently been increased as a result of poor performance of the banks' Third World loans, some of which may never be repaid.

"It {the prime rate increase} basically comes as no surprise," said Elizabeth G. Reiners, a money market analyst with Dean Witter Reynolds Inc. "Banks have been under pressure to maintain profit margins following huge writeoffs for loan-loss reserves."

The last time the prime rate was as high was in March 1986, when it was reduced from 9.5 percent to 9 percent. At the peak in 1981, the prime rate was 20.5 percent.

Greenspan is said to feel that the danger of inflation has been exaggerated by some analysts, and that the scare over possible high interest rates has been overdone. In a television interview Sunday he said that "the current reality" is working against the markets' expectations of inflation, and that "we might find interest rates starting down."

Fed officials are much more concerned -- and to some extent puzzled -- by the rise in long-term rates. The yields on long-term Treasury bonds are at the highest levels in two years. Three-year Treasury bonds on Tuesday yielded about 9.78 percent, compared with 9.20 percent in early September and an average of 7.39 percent in January.

On "This Week With David Brinkley" Sunday, Greenspan said: "One thing that's puzzling me ... is ... a fear that now we've gotten inflation under control, the next step is to get it out of control again. ... And what that has done, it's created what economists call an inflation premium embodied in long-term rates. And that, I must say, bothers me, largely because at the moment, there just is no sign inflation is picking up."

Nonetheless, markets have been jittery over the possibility that Greenspan's hand might be forced by a higher interest rate trend in Germany and Japan. To keep the heavy flow of foreign investment into dollar-denominated securities coming, observers say, the Fed might have to raise the discount rate again.

Rising rates have also jarred the stock market, where there is fear is that higher interest rate costs will slow business investment and expansion. And traditionally, higher returns in the bond market tend to pull money out of stocks. Such a movement is said to have been a factor in Tuesday's stock market collapse. But yesterday, after an erratic day, the Dow Jones industrial average closed with a small gain.

Meanwhile, the average yield on the Treasury's auction of $6.76 billion in seven-year notes yesterday was 9.51 percent, marginally higher than had been expected. At the last auction of seven-year notes, on June 25, the average yield was 8.10 percent. The jump of almost 1.5 points in that short time is indicative of bearish market sentiment.

The banks' prime rate was last raised, from 8.25 percent to 8.75 percent, on Sept. 4, the day after the Federal Reserve boosted the discount rate from 5.5 percent to 6 percent. The Fed's action was widely interpreted as a signal that the central bank would work against inflation, and that it desired to strengthen the dollar in foreign exchange markets.

Since then, financial markets have been anxious, and many analysts have predicted that further discount rate increases were on the horizon.

The banks have now increased the prime rate four times in 1987 in response to their own higher cost of borrowing money and to cover the higher interest they have been paying on some deposit accounts. As recently as April, the prime rate was only 7.5 percent. Other rates also have soared, including mortgage rates, which now exceed 11 percent.