Despite strong pressure from the Carter administration to reduce interest rates, many of the nation's major banks today raised their prime lending rate to 14 percent from 13 1/2 percent.

President Carter and many of his chief advisers have criticized both bankers and the Federal Reserve Board for the high interest rates and have charged that high rates threaten to undermine the fledgling economic recovery.

As recently as Thursday, Treasury Secretary G. William Miller complained that high interest rates threatened a recovery in both the housing and construction industry and the automobile industry. He said that under current circumstances banks should look to lowering their prime lending rates "at the earliest opportunity."

Instead, led by Chase Manhattan Bank today, many of the nation's biggest financial institutions did just the opposite. Citibank, the nation's second-biggest, posted a prime lending rate of 14 percent two weeks ago, but no major banks followed Citibank's lead until today, presumably because of the heavy political pressure.

Even Federal Reserve Board Chairman Paul A. Volcker, who was publicly chastised by the president for pursuing a monetary policy that boosted interest rates to exorbitant levels, was critical of the banks. Volcker said that interest rates had risen to levels that weren't justified by the central bank's policy actions.

In announcing the increase in the interest it charges its best corporate customers for a short-term loan, Chase said that "other market interest rates have continued to increase and loan demand has been growing. Our change in the prime reflects Chase's continuing policy to adjust the rate to reflect changing market conditions."

Chase added that it made its move "after considerable thought" but said a rise to 14 percent "at this time is clearly warranted and appropriate."

At a bankers convention in Chicago earlier this week, Chase Chairman David Rockefeller predicted that interest rates would move down between now and the rest of the year because the money supply, which had been growing swiftly during August and September, was beginning to contract.

However, late today the Federal Reserve reported that M1-A, the basic measure of the money supply, grew $4.1 billion in the week ended Oct. 8. A wider measure, M1-B, grew $5.1 billion. (Story and tables, D5). The money supply -- essentially cash and checking accounts -- is a major influence on both inflation and output. Most economists agree that if the money supply grows too quickly it results in a rising price level.

The Federal Reserve, through its monetary policy operations, tries to keep the money supply growing on a track the central bank feels is consistent with reducing inflation.

The administration, which had made fighting inflation its primary economic goal, had remained mum about the Federal Reserve's policies and even supported them when interest rates went as high as 20 percent last spring. But in mid-April rates began to drop swiftly, and the prime rate declined from 20 percent to 11 percent in a three-month period.

Then interest rates in the open market began to rise again, and by August banks were starting to raise their prime rates in response. Because banks borrow on the open market most of the funds they lend to customers, when rates on financial instruments, such as certificates of deposit, begin to rise the costs to banks begin to rise as well.

After an explosion in money growth in early August, the Federal Reserve began to tighten its policies, and as a result rates rose even faster.