Nearly all of the nation's major banks raised their prime lending rates to 14 1/2 percent from 14 percent today, a move they would have made Tuesday but for the presidential debate, banking industry sources said.

Banks have been under heavy pressure from the Carter administration to hold down lending rates. President Carter and his economic advisers have said they fear higher rates will choke off the incipient economic recovery.

Late today White House Press Secretary Jody Powell said that banks seem "more interested in raising prime rates than lowering them" and called the case for the increase "a very shaky one."

Banks said that sharp increases in the cost of obtaining funds dictated an increase in the interest they charge their best corporate customers for a short-term loan. Rates in the open market have jumped sharply in the last week, because of a tighter monetary policy by the Federal Reserve and because of renewed fears of inflation.

"Contrary to what Mr. Powell said, the markets called for an increase to 14 1/2 percent or more on Tuesday. But no bank had the nerve to raise the prime in the face of the debate and without knowing how much of the nation's economic woes would be blamed on the banking system," said an official of one major bank. "It's also fair to say that no bank wanted to give President Carter a political football just before the debate either." t

Interest rates were not mentioned in the 90-minute debate between Carter and Republican challenger Ronald Reagan, but Powell told reporters that if the president had been asked about them he would have questioned whether bankers could make a case for raising their interest charges.

The banks had barely opened their doors this morning, however, when financial institutions began announcing increases in their prime lending rate. Morgan Guaranty Trust Co., the nation's fifth-biggest, lead the parade at 9:30 a.m., and by noon everyone of the nation's 10 biggest banks and most of the rest had increased the rate to 14 1/2 percent. Riggs National Bank in Washington, the largest in the D.C. area, said its prime would go to 14 1/2 percent Thursday morning.

A spokesman for Chase Manhattan Bank said the increase was caused by a "continued increase in market interest rates." But he cautioned that today's rise "should not be construed as predicting the future course of rates."

Home mortgage loan rates also increased today. The Federal Home Loan Mortgage Corp. reported that for the first time since April, mortgage rates went over 14 percent at its weekly auction. The mortgages the corporation agreed to purchase today will carry an average rate of 14.22 percent.

Charles Shultze, chairman of the Council of Economic Advisers, told reporters this morning -- before the prime rate increases were announced -- that most economists expect interest rates to begin to decline over the next few months.

Nicholas Marrone, assistant treasurer of the Bank of New York and one of the bank's chief money traders, said he thought the half-point increase in the prime rate was "quite modest" in view of the sharp increases in costs banks have faced.

The interest banks must pay on the funds they borrow to loan to customers have jumped from about 12.50 percent a week and a half ago to about 14.20 percent today. Most of the money banks lend to their business customers is obtained by issuance of large-sized certificates of deposit.

Interest rates were driven up further in late money market trading after the Treasury Department announced that it plans to raise $8 billion next week, including more than $3 billion of new cash.

"I wouldn't say that was a lot more than the markets anticipated," Marrone said, "but it is a big chunk of financing at a time when the markets are not performing very well."

Not only have rates skyrocketed in the short-term money markets, they have climbed in the long-term markets, as well. Businesses, utilities and local governments have been canceling or reducing proposed bond offerings because of high interest rates and the unwillingness of investors to purchase new bonds.

As a consequence, the frustrated bond sellers have been turning to their bankers for short-term loans until bond rates go down. That has increased loan demand at banks during the last six weeks, putting further pressure on them to raise their rates.

However, a spokesman for Chase Manhattan said, this week loan demand has not increased, but has held steady.