Stock prices slumped for a second day in a row today as rising interest rates threatened the economic recovery and many big investors continued to sell stocks to realize profits.

The Dow Jones industrial average fell 11.18 points to close at 974.75. On Friday, the day after the average climbed above the 1,000 barrier for the first time since 1976, the Dow average declined 10.24 points.

"The market has an awfully good run, gaining 70 points in two weeks. It had to come down," according to Larry Wachtel of Bache Halsey Stuart Shields Inc. However, Wachtel said, the market remains strong despite the recent declines.

"I look at Friday and today as nice pullbacks, and I could even countenance another decline tomorrow [Tuesday]. But by Wednesday, or Friday, I expect another rally. The market always does well the day after Thanksgiving."

The market ralied for two weeks following the election of Ronald Reagan as president. But by Friday, even the Reagan euphoria could not blot out of investors' minds the sharp rise in interest rates that has occurred in the last week -- during which the prime lending rate has climbed from 15 1/2 to 17 percent.

Higher interest rates threaten the economy -- bad news for corporate profits and stock prices -- and also make it more expensive for investors to borrow money to buy stocks.

A report from the Federal Reserve today that the money supply jumped $1.8 billion last week convinced many investors that interest rates would rise further before they decline as the Fed continues to fight inflation by tightening monetary policy.

Besides the fear of interest rates, stock prices also were hurt by "programed selling" by many big institutional investors, who decided to sell some of their stock holdings when the Dow average hit 1,000 to take profits on stocks that have risen sharply, not only in the last 2 1/2 weeks but for the last seven months. Even after the last two days of decline, the Dow average is 200 points higher than it was in mid-April.

Stock prices made a small try at a rally in late trading. The Dow average was down 16 points at 1 p.m. and 15 pointss at 2 p.m., only to close down 11.18.

Trading volume, which had been running at a record pace during the two weeks following the presidential election, slowed Friday and slowed further today, although it remains heavy by historical standards. Investors bought and sold 51.4 million shares today, compared with 56 million on Friday. bEarly last week trading volume averaged 70 million shares a day.

The number of stocks which closed lower today outnumbered the gainers by 1,114 to 478 on the NYSE.

On the American Stock Exchange, the index closed down 2 points at 356.44, with 185 shares closing higher and 439 declining.