Stock prices rose sharply today as investor worries about rising interest rates eased.

The Dow Jones average of 30 industrial stocks rose 15.02 points to 965.70.

The market rally was led by oil company stocks, but the increase was broad-based. On the New York Stock Exchange 1,263 stocks closed higher in price while only 381 declined.

The lessening of investor fears in rising interest rates also helped bond prices, which rose in nearly every market -- U.S. government, municipal and corporate.

Nevertheless, because bond prices have fallen so sharply in recent weeks -- due to rising interest rates -- the number of companies and local governments trying to sell bonds has been reduced sharply. Southern Bell Telephone & Telegraph announced today it will reduce to $300 million from a planned $450 million its offering of bonds scheduled for Tuesday. Late today the company priced its bonds to yield 12.94 percent.

Since reaching a low point in early July, market interest rates have climbed sharply both in response to Federal Reserve Board tightening of monetary policy and because investors felt the central bank was losing control of money supply growth and would have to tighten further.

Last Thursday President Carter sharply critized the Federal Reserve for permitting interest rates to rise as fast as they have. The following day, Fed Chairman Paul A. Volcker critized banks for pushing the prime rate up so fast, arguing that money market conditions did not justify a prime rate of 13 1/2 percent.

The same day, Citibank, New York's largest, raised its prime lending rate -- the interest it charges its best corporate customers for a shortterm loan -- to 14 percent. But no other major banks have followed Citibank's lead, and today a small bank in St. Louis cut its prime rate to 13 1/4 percent.

Investor fears were assuaged further after the market closed last Friday when the Federal Reserve announced that the money supply fell sharply in the week ended Sept. 24.

When interest rates rise, bond prices fall; if rates rise high enough and fast enough, stock prices often fall, as well. High interest rates make it more expensive for investors to buy securities on credit and also make investments such as government securities, which are virtually riskless, more attractive than stocks.

But the black mood that prevailed on Wall Street early last week had turned to a bullish one today. Between Sept. 24 and last Monday, the Dow index lost nearly 50 points. By the close of trading today, the index had recovered almost to the 974.57 peak registered on Sept. 24.

Other indexes also pointed to a bullish attitude on Wall Street. The New York Stock Exchange's own index was up 1.30 points to 76.04, while the American Stock Exchange index closed up 6.23 points at 346.62.

On the Amex, 455 stocks closed higher while only 183 declined.

Oil companies were the hottest issues today. Exxon closed up 2 1/4 at 75 1/4, Mobil was up 2 7/8 to 75 1/2, Standard Oil of California climbed 2 1/4 to 86 3/4, while Texaco rose one point to 37 1/4.

With gold prices rising, precious-metals stocks also gained. ASA picked up 2 1/4 to 87 1/4, Dome Mines added 4 1/2 to 123 1/4 and Homestake Mining was up 3 7/8 to 72 3/8.

More than 50.2 million shares changedhands on the New York Stock Exchange, up from 47.5 million.

Since last Monday, when the Dow average closed at 921.93 (down 18.17 points on the day), the index has climbed 43.77 points.