Most of the nation's major banks boosted their prime interest rates to a record 12 1/4 percent from 12 percent today, as heavy loan demand and tight monetary policy continued to push up interest rates.

Last week, most banks raised their prime rates -- the interest they charge their best corporate customers for short-term loans -- to 12 percent, matching the record level reached in July 1974 during the severe credit crunch that preceded the last recession.

Both today's and last week's increases were touched off by New York's Chase Manhattan Bank, the nation's third largest.

The increase came as no surprise to analysts, who say the rate almost inevitably will move to 12 1/2 percent by the middle of September and perhaps as high as 13 percent before the Federal Reserve Board lets up on the tight money policy designed to fight inflation by cutting down on the expansion of credit and the growth of the money supply.

Last Friday, the Federal Reserve tightened its money policy for the second time in two weeks by raising the interest target on its key federal funds rate from 11 percent to 11 1/4 percent.

The Fed controls the federal funds rate -- the interest banks charge one another for overnight loans of excess reserves -- by buying and selling government securities on the open market. When it wants to raise the rates, it simply stops buying securities (an action which injects funds into the banking system) until the rate rises to a level that is consistent with the Federal Reserve's goal.

The week before last, the Fed boosted the federal funds rate from 10 5/8 percent to 11 percent and also raised its discount rate -- the interest it charges member banks to borrow from the Fed -- from 10 percent to a record 10.5 percent.

Although the prime rate and the discount rate are at record levels -- and most other short-term rates are at or near their 1974 peaks -- plenty of credit still is available in the financial system, albeit at a high price.

Analysts say that, although the nation's central bank is concerned that raising interest rates too high could throw the nation into a severe recession, it has no choice at the moment but to continue with a tight money policy.

The money supply -- checking accounts and currency in circulation -- jumped $1.8 billion last week despite the tight money policy, and commercial and industrial loans grew sharply at New York banks.

Although all economists don't put the same emphasis on the role of the money supply in inflation, all agree that it adds to inflation when it increases too quickly -- and it is growing at a 9 percent annual rate now, twice as fast as the Federal Reserve wants it to. Loans also are growing more rapidly than the government desires.

In 1974, by contrast, credit was hard for businesses and individuals to come by and home mortgage loans nearly were unavailable.Today, although mortgage rates are 11 percent or more in many parts of the country and harder to get than a year ago, home buyers usually can find financing if they are willing to pay the price.

Among the banks that joined Chase in raising their prime rates today were Bank of America of San Francisco, the largest; Morgan Guaranty, Chemical, Irving Trust, Marine Midland, Bankers Trust, European American and U.S. Trust Co. of New York; Continental Illinois, Harris Trust and Northern Trust of Chicago; Security Pacific and Union Bank of Los Angeles; First Pennsylvania and Girard of Philadelphia; and Mellon and Pittsburgh National of Pittsburgh.

Citibank, New York's biggest bank and the second largest in the nation, sets its prime rate each Friday based on a formula that relates to it cost of obtaining funds. First National of Chicago, which also uses a formula, announced Monday that it wouldn't raise its prime rate but will review it Friday because Monday is a holiday.

Both major banks are expected to raise their prime rates this Friday.

Although White House inflation monitors criticized banks and the Federal Reserve a year ago -- when the federal funds rate was about 8 1/2 percent and the prime rate about 9 percent -- since the White House has acquiesced in a year of rising interest rates.

The Fed is raising interest rates not only to try to stem domestic inflation but also to atabilize the value of the dollar in foreign currency trading.