Investor euphoria about declining interest rates fueled a broad-based rally on the stock market yesterday in which the Dow Jones industrial average cracked the 1,300-point mark and set a record closing level.

The Dow, which previously traded above 1,300 but never closed over 1299.36, finished the day at 1,304.88, an increase of 19.54 points from Friday's level. But analysts said the performance by the bellwether average only validated a strong rally that has been going on for several days.

"Everybody focuses on the Dow, but all last week you had new highs in the Standard & Poor's 500 and other broader-based market indices," one trader said. "The Dow clearly had to catch up."

The market's rise was given new momentum after the close of trading Friday, when the Federal Reserve cut the discount rate to 7 1/2 percent from 8 percent. Banks across the nation echoed that cut yesterday by reducing their prime lending rates to 10 percent from 10 1/2 percent.

Analysts had expected the Fed to reduce the discount rate in an effort to stoke the increasingly sluggish economy, but they hadn't expected the reduction to come until later this week. "There's no question that this had been hoped for. The surprising thing was that it came as quick as it did," said Charles Jensen, a market analyst for MKI Securities. "This allowed a lot of money to come into the market that was undecided."

"The market was looking for some sort of jolt to signal that the Federal Reserve also recognized the sluggishness of the economy and was willing to do something about it," said Monte Gordon, an analyst at Dreyfus Corp. "The market is interpreting the Fed's action as a signal that the Fed is concerned about the state of the economy."

The analysts cautioned, however, that the Fed might have to take additional steps to reduce interest rates following this week's meeting of its Federal Open Market Committee to convince the stock market that an improvement in the economy is truly at hand. "It's not a fait accompli," Gordon said. "Everything has not been put into place."

Lower interest rates help the stock market in two ways: by improving the economy and, in turn, the profits of corporations whose stocks trade in the market, and by making interest-bearing investments such as bonds or money market funds less attractive, thus driving investors to more attractive investments in the stock market.

Investors seemed happy enough yesterday with the lower interest rates. Composite volume in issues listed on the New York Stock Exchange was a whopping 170.99 million shares, and every major market index showed strong gains, with many setting records. There were three advancing issues for every declining one on the NYSE, and 449 of the more than 2,000 issues traded on the Big Board hit new highs -- while only eight hit new lows.

The NYSE's composite index gained 1.24 points to reach a new high of 109.72. Standard & Poor's index of 400 industrials went up 2.90 points to 209.86, and S&P's 500-stock composite index rose 2.30 points to a record 189.72.

The Nasdaq composite index for the over-the-counter market gained 2.78 points to 294.48, while the American Stock Exchange's market value index closed at 232.77, up 2.01 points.

All but two of the blue-chip issues that make up the 30-stock Dow Jones industrial average showed increases on the day, including General Motors, which climbed 1 5/8 to 70 3/8; General Electric, which rose 1 3/4 to 61 3/8; United Technologies, which increased 1 3/4 to 41; and Minnesota Mining & Manufacturing, which gained 1 3/4 to close at 78.

The rise in the industrials only reflected the gains over the past few days in the faster-moving high-technology growth stocks, which tend to lead the market. "The Dow is 30 stocks, mostly manufacturing companies , and the action in the economy is out of manufacturing," said one broker.

Among technology issues, Burroughs was up 1 5/8 to 65 3/4, Hewlett Packard rose 1 7/8 to 36, and IBM, a Dow Jones average member, shot ahead 2 1/4 to 132 3/4. General Motors' "E"-class common stock, which is designed to reflect the performance of the company's high-tech Electronic Data Systems subsidiary, soared 5 to 78.

The day's most active issue on the NYSE was American Telephone & Telegraph, which gained 3/4 to 24 1/4, a new 52-week high, on a volume of 2.5 million shares.

Stocks in companies that could benefit from lower interest rates were among the day's best performers. Home builders and building-supply companies such as Standard-Pacific and Pulte Home showed gains of $1 or more.