Continued high interest rates, new confusion about the Reagan administration's economic policy, and renewed fears about the stability of the government securities market today pulled the Dow Jones industrial average to its lowest point in three months as stock prices fell broadly.

The average fell 11.52 points to just under 805, its lowest point since mid-March, as the average price per share on the New York Stock Exchange dropped by 41 cents. The Dow average of 65 blue-chip stocks fell 4.38 to 315.49.

The daily tally on the New York Stock Exchange showed more than three losers for every stock that rose in price, and the NYSE's composite index slumped 1.00 point to 63.42.

Standard & Poor's index of 400 industrials dropped 2.01 points to 122.89, and S&P's 500-stock composite index was down 1.77 points at 110.09.

Big Board volume totaled 44.11 million shares, down from 48.45 million Thursday. Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 51.46 million shares.

The American Stock Exchange market value index lost 4.32 points to 258.98, while the NASDAQ composite index for the over-the-counter market closed at 174.82, down 2.28 points.

"The psychology has turned very sour," said Jerry M. Hinkl,e chief trader for Sanford C. Bernstein and Co. "The confusion could turn to paralysis, and many people are wondering if there really is going to be an economic rebound."

Wall Street also may have been jarred by published reports that Joe Granville, the flamboyant stock analyst, is predicting that the Dow industrial average might drop to 650, rally slightly and then fall again sharply.

"It's as if you hit somebody when he's already reeling," noted Hildegard Zagorski, second vice president of Bache Hasley Stuart Shields Inc. "The failure of interest rates to come down, the failure to get a workable federal budget, and a sharp decline in commodity prices make for a lot of negatives over a recent period of time."

The news about Marine Midland suspending and then resuming trading for Comark, a California government securities dealer, also set off further selling late today. "It was one more thing to throw into the pot," Zagorski noted.

The day's news brought to a close a gloomy week on Wall Street, with the industrials falling more than 14 points over the period.