Fears of a severe recession and high, inflation-producing budget deficits triggered a steep decline in both the stock and bond markets today.

The Dow Jones industrial average -- the most carefully watched indicator of stock market activity -- fell 20.45 points to 900.11, its lowest level since July 11, 1980, when it closed at 891.13..

The decline in stock prices was widespread. On the New York Stock Exchange, 1,552 issues closed lower, while only 143 were higher. But there was no panic-selling. About 46.8 million shares changed hands on the NYSE, not an abnormally high volume for recent years. Friday's volume had been 37.67 million shares. Today's composite volume was 54.19 million shares.

In the bond market, prices fell to record or near-record lows. According to Andrew Morse of the brokerage firm Drexel Burnham Lambert Inc., the average bond lost $20 for each $1,000 of its face value.

Analysts said that investors are more anxious than ever about President Reagan's new tax cut bill. "Wall Street never embraced the full Reagan program," said Newton Zinder of the brokerage firm E.F. Hutton & Co. Inc.

The administration now concedes that budget deficits will be higher than projected as a result of the tax cuts, and it is looking for new ways to trim the budget.

With tax rates now indexed to consumer prices, future tax cuts are now automatic, "while spending cuts still rely on the cooperation of Congress," said Richard Hoey, an analyst with Bache Halsey Stuart Shields Inc.

That upsets investors, who feel the government will have to finance more debt than was anticipated. Heavy government borrowing helps keep interest rates up and makes it more difficult for businesses and local governments to borrow funds.

Investor worries are compounded by continued high interest rates that many fear will produce a recession that is sharper than most economists have been projecting. Despite a marked slowdown in the rate of inflation in recent months, interest rates have remained high. When interest rates were at or near the rate of inflation, business could hope to recoup in higher prices and workers in higher wages much or all of the cost of borrowing. But today interest rates are 10 percentage points or more higher than the rate of inflation.

A recession is bad news for stock prices because profits slump and bad news for budget deficits because tax revenues begin to fall just as government spending on items such as unemployment start to rise.

Hopes have waned that the Federal Reserve, the nation's central bank, would begin to ease up on its tight money policy that has kept those interest rates high.

But last Friday the Federal Reserve reported that the money supply rose $800 million in the week, following a steep $5.1 billion increase the week before. Most economists think that inflation and the growth of the money supply are inextricably related. If money grows too fast, so do prices.

As a result, it is unlikely that the central bank will allow interest rates to fall as analysts had hoped, said William Sullivan, vice president of the Bank of New York. However, Federal Reserve officials consistently caution against reading too much into one or two weeks of money supply figures.

For the year as a whole, the money supply still is growing more slowly than the Fed's targets, and if the Fed fears a severe recession, it may decide to ease up on the interest rate reins.

But the stock and bond markets do not believe that will happen. Investors seem to believe, correctly or not, that the twin evils of inflation and recession will reoccur.

"The market is saying 'Show me. I'm cynical'," said Drexel Burnham's Morse.

The New York Stock Exchange's own index was down 2.18 points to 72.92, while the American Stock Exchange index was off 12.13 points to 352.52.

Oil company stocks were among the most active on the New York exchange, in part because of the inability of oil-producing countries to reach agreements on prices and production. Exxon was the most active, as 828,500 shares changed hands. Exxon fell 1 1/8 to 33 1/8. Mobil was down 1 3/4 to 28 1/4, while Standard Oil of California dipped 2 1/8 to 41 3/8.

Only in the short-term money markets was there relative stability, mainly because the Federal Reserve today held the key interest rate, the federal funds rate, stable at 17 3/4 percent, according to Bank of New York's Sullivan.