Interest rates, which had declined most of the day because of a good report on inflation from Washington, shot up again in late bond and money-market trading after the Federal Reserve reported money supplies declined following last week's explosion.

Investors and traders think that the relatively modest decline in money will probably force the Federal Reserve to run a more stringent monetary policy in the weeks ahead. A tighter monetary policy usually spells higher interest rates.

Meanwhile, the stock market started strongly but lost ground in late trading. The Dow Jones Industrial Average, which had been up 10 points in heavy trading at 2 p.m., lost about 7 points in the last two hours to close up 3.16 at 958.19. Trading was heavy.

Monte Gordon of the Dreyfuss Corp. said investors became cautious in the final hours of trading in anticipation of the 4:10 p.m. announcement on the money supply that came from the Federal Reserve. The stock market closed at 4 p.m.

Although trading in stocks was exceptionally heavy for a Friday in August, trading in the money and bond markets was light.

In another development, most of the nation's major banks boosted their prime lending rate to 11 1/4 percent from 11 percent, a move that was initiated by Chase Manhattan Bank last Tuesday.

Banks, which have to buy most of the funds they lend in the open market, have seen costs rising sharply in the last few weeks because of the increase in short-term interest rates.

William Sullivan, vice president of the Bank of New York, said that after the Fed announced that the money supply grew faster last week than first reported and that the decline in the money supply this week was smaller than many had hoped, interest rates rose and bond prices fell.

Sullivan said that Treasury bill rates had dropped 15 to 20 basis points (a basis point is one one-hundredth of a percentage point) after the Labor Department announced that the consumer price index did not rise at all in July, the first time in 13 years that there was no increase in overall consumer prices.

Bond prices had risen about $7.50 per thousand dollars of face value, recovering nearly all they had lost in Thursday's trading.

Sullivan said that when the money supply figures were announced, both the money markets (where short-term debt securities are traded) and the long-term bond markets lost all their gains of the day.

The Federal Reserve said that the money supply -- cash in circulation and checking accounts at commercial banks -- fell $3.6 billion in the week ended Aug. 13. But the central bank revised upward the money supply figures it reported for the week ended Aug. 6. Last week the Fed said the money supply was $381.5 billion; this week the Fed said the figure should be $382.9 billion.

That means that this week's decline of $3.6 billion is less than it seems. Measured off last week's original report the dip in the money supply is only $2.2 billion.

The rate at which the stock of money grows is critical both to the pace of inflation and the level of economic output and jobs.

Analysts thought the money supply might fall as much as $5 billion this week because there were flukey factors in last week's record increase, mainly an early payment of Social Security benefits that sat around in checking accounts an extra two days.

"The market construed today's report unfavorably," Sullivan said.

Even though the Federal Reserve cautions against taking a single week's figures seriously, the markets fear that the Fed will have to take stronger actions to reduce the expansion in the money supply in its fight against inflation. For the last four weeks the money supply has been growing at an annual rate of 11.8 percent, far in excess of the Fed's third-quarter target of 7 percent. A broader definition of money -- which includes NOW accounts at banks, savings and loan associations and mutual savings banks -- has been growing at a 14 percent annual rate.

More than 58.5 million shares of stock changed hands in heavy trading on the New York Stock Exchange, compared with 50.9 million shares Thursday. On the NYSE, 991 stocks closed higher, while 543 closed lower. The New York Stock Exchange composite index was up 0.40 point to 72.47.

Some analysts attributed part of the late slippage in stock prices to a less-than-glowing report by Mobil Oil Corp. on a well it has been drilling off the coast of Newfoundland.

Trading in Mobil was halted for a time. When it resumed, the price fell sharply and the oil company closed the day off $1.625 a share. Earlier in the day, Mobile had been up about $1 a share.

On the American Stock Exchange, the index closed up 1.06 points to 332.15. Nearly 390 Amex stocks gained in price while 248 closed lower.