The Dow Jones Industrial average fell by almost 16 points today as last week's reported jump in the money supply and some selling pulled stock prices down for the fourth consecutive Monday session.

Several analysts suggested that unless the market opens strongly tomorrow, the steep "correction" long predicted on Wall Street might come to pass. "It's important that the market show its stuff tomorrow," said Larry Wachtel, stock analyst at Prudential-Bache Securities Inc. "If it doesn't, we could see a five to seven percent retracement."

The losses today come just after last week's fall in the industrial average of close to 14 points, the first weekly loss of that measurement since early April. In the period from April 6 to May 6, the average, the most carefully tracked market barometer, rose by 122 points.

But Wachtel also suggested, however, that there was little evidence today of selling by major institutions as volume on the New York Stock Exchange totaled only 76.2 million shares, down from the 83.1 million reported Friday. "That says to me that those were nervous Nellie individuals selling rather than institutions," Wachtel said.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 87.32 million shares.

The market's recent pattern of losses early in the week followed by advances seemed in evidence again today as Dow industrials, at one point during the day off by 22 points, picked up steam to close 1,202.98, down 15.77 points. The New York exchange composite index fell 0.88 point to 94.19 and the average price per share dropped by 35 cents. The Standard & Poors index of 500 stocks fell 1.50 points to 163.40.

Yet the losses were also broad, as 1,269 stocks fell, 407 rose and 298 were unchanged. Of the 30 stocks in the Dow industrial average, 27 declined, as did 19 of the 20 issues in the Dow transportation index.

On the American Stock Exchange, the average price per share dropped 22 cents, as the Amex index fell 5.76 points to 446.20. Volume was 10.4 million shares, down from 11.15 million Friday as 456 Amex issues fell and 201 advanced.