Major U.S. banks lifted their prime interest rate another quarter point to 9 1/4 percent yesterday as the cost of borrowing money continued to rise.

With yesterday's action, the cost of short-term credit has gone up nearly 20 percent since the start of the year.

The Chase Manhattan Bank initiated yesterday's step, with other large banks quickly following suit. The prime rate is the one banks charge their most credit-worthy customers. Chase said it had raised the prime "because the cost of our funds went up."

That was the result of actions by the Federal Reserve Board, the bank said. The Fed has been moving to restrict the supply of credit and drive up interest rates as a way of fighting inflation and propping up the dollar.

The last time the prime rate stood at 9.25 percent was in Feburary 1975, on the way down from the record peak of 12 percent hit in 1974, when the Fed slammed down hard on the credit brakes and contributed to the steep recession that began late that year.

Most analysts doubt that the prime rate will approach that record level during the current economic cycle. At a Chicago conference yesterday, Michael K. Evans of Chase Econometrics Association Inc. and Robert Gough of Data Resources Inc. predicted that interest rates would peak later this year and drop somewhat in 1979.

But analysts add that the Fed faces an increasingly difficult policy in continuing to use higher interest rates to dampen economic activity and ease inflation without inducing a recession.

In efforts to both defend the dollar and moderate domestic inflation, th Fed has raised the key federal funds rate three times in the last two weeks, boosting it to 8 percent from 7 7/8 percent. It started the year at just over 6 1/2 percent.

The Fed uses the federal funds rate, which banks charge each other for short-term loans, as its benchmark for controlling the country's money supply. An increase in this rate quickly ripples through the entire interest rate structure.

Meanwhile, the basic inflation rate seems to be rising, rather than moderating, despite the reported slowdown in the consumer price index for July. Fed Governor Henry Wallich said yesterday that inflation has accelerated "from the 6 percent area into the 8 percent area" and that fiscal monetary policy has not "succeeded in decelerating it."

Wallich reiterated his support for an anti-inflation program that would use the federal tax system to reward businesses that keep a lid on prices, and penalize others who raise them.

Fed Chairman G. William Miller last week asked President Carter to consider an "anti-inflation tax" on excess business profits as another possible anti-inflation tool.

The dilemma facing the Fed is that the increases in interest rates this year have so far not done much to deter borrowing by either consumers or businessmen, or to cool inflation.

And some have accused the Fed of fueling inflation by increasing the basic money supply too fast.

At the same time, some analysts say the point is approaching where further increases in interest rates could trigger an economic downturn as mortgage funds dry up and hurt the housing sector and businesses decide to postpone borrowing that would finance expansion.

"At a funds rate above 8.5 percent, the Fed is going to be concerned about the impact of further tightening on the domestic economy," said William Gibson, an analyst with Smith Barney, Harris Upham & Co. "The underlying economy is not that strong, and I don't think the Fed wants to send the economy into a full-fledged recession.

Recent government figures showed some sharp drops in factory orders and in durable goods sales. And some analysts expect the index of leading indicators, scheduled for release today, to show a drop of more than 1 percent, pointing to a significantly weaker economy in the months ahead.

At the same time, consumers and businessmen have continued to borrow heavily to finance home purchases and construction, apparently hoping to keep one step ahead of what they believe will be even higher borrowing costs in the months ahead.

The F.W. Dodge division of McGraw-Hill Information Systems reported yesterday that July construction contracts totaled $14.7 billion, with both residential and nonresidential construction recording massive gains. The overall total was up 36 percent from July 1977.

George Chrispie, Dodge chief economist, said July was "a typical month for the booming construction industry, showing all of the market's current traits: a very high total volume, steadiness in housing at the 2-million-unit level, surging commercial and industrial building and an erratic flow of heavy construction projects."

"The Fed must be disappointed that it hasn't had the retarding effect it hoped on what may be a demand-pull inflation" from its higher interest rate policy, said Leonard Santow, senior vice president with the J. Henry Schroder Bank & Trust Co.

"The consumer is out there borrowing and spending in anticipation of even higher prices," he said. "The Fed would like to see some marginal dropoff in consumer demand, but it's not getting as much bang from the buck as it hoped."