The stock market fell sharply today amid increasing investor concern over the potential for rising interest rates and growing speculation that Federal Reserve Board Chairman Paul A. Volcker will not be reappointed.

The Dow Jones Industrial Average fell 19.33 points to 1,194.91, its biggest loss in five weeks.

"A lot of guys are shooting their mouths off leading the market to believe there might be a new Fed chairman," said William LeFevre, vice president for investment strategy at Purcell Graham & Co. Inc. "The market does not like indecision and uncertainty."

Investment managers continued to suggest that with the passage of time, the reappointment of Volcker, whose term expires in August, seems less likely.

"Things are a little bit in limbo on the monetary side," said Lee H. Idleman, director of research at Dean Witter Reynolds Inc. "We are out on the end of a limb with regard to the Fed chairmanship. The longer time goes by chances are perceived to be less that he Volcker returns."

Interest rate fears were prompted in large part by the announcement that the Federal Housing Administration is raising the maximum rate on single-family mortgages it will insure from 11.5 percent to 12 percent. There was increasing speculation on Wall Street that broader interest rate increases might be forthcoming.

In addition, Fed member Henry Wallich raised new concerns about the federal deficit when he told a Washington audience that "large budget deficits drive up interest rates," a notion that most Wall Street analysts had discounted as a short-term factor in the current stock market.

Although volume on the New York Stock Exchange rose only slightly today from Tuesday's 87.6 million shares to 88.5 million shares, the losses were widespread. Just under 600 stocks rose on the New York exchange, while 1,035 lost.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 101.84 million shares.

The New York composite index closed down 1.03 points at 94.37, and the average price per share fell by 40 cents. Standard & Poor's index of 400 industrials fell 2.42 to 182.73, and S&P's 500-stock composite index was off 2.06 to 162.77.

But the Dow Jones average of 20 transportation stocks, led by strong airline gains, climbed 1.39 to 558.58, matching its record high set last May 25.

The American Stock Exchange index closed down 2.95 points to 464.86. Volume rose to 11.9 million shares from 10.7 million Monday. Declining stocks outnumbered advancing issues by 358 to 297 and the average price per share on the Amex was down 11 cents.

On the over-the-counter market, the NASDAQ composite index closed down 1.31 points to 314.17.