Stock prices fell sharply in the first hour of trading yesterday and then seesawed before closing sharply lower as nervous investors looked for some sign that the Federal Reserve Board would take steps to reduce further the level of interest rates.

The market rallied after a 3 p.m. news report that the White House had predicted the Federal Reserve would cut rates later in the day. The rally faded when both the Fed and the White House denied the report.

The Dow Jones average, which measures the performance of 30 widely owned industrial stocks, closed at 1008.00, down 13.43 points from Monday. In early trading, the Dow had been down as much as 22 points; during the rally, the loss had been narrowed to 5 points.

Big Board volume totaled 102.91 million shares, up from 78.90 million on Monday. Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 118.58 million shares.

But the money markets, which continue to trade long after the 4 p.m. closing bell on the New York Stock Exchange, rallied again about 5 p.m., according to Douglas Ledwith, chief financial officer at American Security Bank.

Bond prices, down at about $5 for each $1,000 of face value at 4:30 p.m., ended the day up about $5. The federal funds rate, the key short-term interest rate, fell to about 9 1/4 percent from 9 5/8 percent, and other short-term rates also declined during late trading.

Late in the afternoon, the Fed injected lendable funds into the banking system, a move that usually signals an easing in central bank policy. But that action got lost for a while in the confusion over the reported White House prediction of a cut in the Fed's discount rate and the subsequent denials of those statements, Ledwith said. Larry Speakes, deputy White House press secretary, whose comments yesterday to reporters caused the confusion, said he had been misunderstood.

But once investors calmed down and looked at the Fed's steps, rates fell, Ledwith said. He said analysts now expect that the Fed soon will cut the discount rate, the interest it charges financial institutions to borrow from it. That rate is 9 1/2 percent today. In late July it was 12 percent.

On the New York Stock Exchange, 1,332 stocks declined while 334 rose. The New York Stock Exchange's index fell 1.02 points to 78.3.

On the American Stock Exchange, the index closed at 328.19, down 6.27. Amex volume totalled 8.47 million shares, compared with 8.15 million on Monday. About 140 Amex stocks rose in price, while 540 fell. The NASDAQ composite index for the over-the-counter market closed at 224.97, down 4.37 points.