Budget Director David Stockman said yesterday interest rates quickly will plunge below 10 percent if President Reagan's economic program is enacted.

Stockman's prediction contrasts sharply with a prediction from Treasury Secretary Donald T. Regan last week, who said that rates will remain high for some time.

Most economists believe that if money growth is to be curbed as dramatically as the administration would like, interest rates will have to stay relatively high.But the forecasts underlying last week's economic package assume that short-term interest rates will drop sharply this year to average only just over 11 percent for the year. This compares with the present rate of more than 15 percent on three-month Treasury bills.

Meanwhile interest rates yesterday continued their gradual decline with a further drop in the key prime lending rate of many banks. Continental Illinois, the nation's seventh-largest bank, dropped its prime a full percentage point to 18 1/2 percent. Most other major banks lowered their rates by a half point, to 19 percent. The nation's two largest, Bank of America and Citibank, left their primes unchanged at 19 1/2 percent.

Stockman told reporters yesterday "we believe that if our full economic plan . . . is put into effect, interest rates in the private market, the prime rate and other sources of credit will fall equal to or below" the 8 1/2 percent and 9 1/2 percent rates presently charged by the Export-Import bank "within a very short period of time." He made the comment in the course of defending the administration's proposal to cut Federal subsidies to exporters.

Last Wednesday Regan told reporters that interest rates would probably stay high for some time, despite the president's economic program.

The Federal Reserve, which is committed to slowing money growth, has indicated that it will not let interest rates drop swiftly, market sources said yesterday. But some easing in credit conditions is expected in the next few weeks, as recent money figures show growth has slowed markedly.

The Fed let rates fall quickly last summer in response to falling money stock. But this decline was followed by a further upwards spiral in interest rates and the Fed is reportedly anxious not to have a repeat of that cycle.

A drop in loan demand in the early months of this year has led to lower rates in money markets and reduced bank costs. This in turn has encouraged banks to bring down the prime rate, charged to best corporate customers. But "while the current cost of bank funds could translate to a prime rate of 17 percent, banks are reluctant to go lower because they still have funds obtained at higher rates on the books," commented Nicholas Marrone of Bank of New York.

"It's difficult for us to see how the Fed can allow rates much below where they are, especially since there's still evidence of forward momentum in economic activity," Marrone said. The Fed yesterday tightened market conditions when the federal funds rate, the rate banks charge each other for loans, was at 14 1/2 percent to 15 percent. Just a month ago this rate was at 19 percent to 20 percent.

Money figures are hard to interpret at the moment because of banking changes, chiefly the nationwide introduction of Negotiable Order of Withdrawal (NOW) interest-bearing checking accounts. But it is clear that loan demand has slipped in the face of the rise in interest rates to a record 21 1/2 percent at the end of last year, and money growth slowed.

Nevertheless, if the administration's forecast of renewed economic growth is to be met while inflation comes down only slowly there will be great pressure on the available money stock, making much lower interest rates unlikely, analysts say.