The nation's major banks boosted their prime lending rate to 20 percent today, its highest level since January.

But interest rates in the so-called open market -- where banks, businesses and the government raise money directly from investors -- either declined or were stable, according to Andrew Morse of the big brokerage firm Drexel Burnham Lambert Inc. Morse said that developments over the weekend suggesting that the tax cut proposed by President Reagan will be scaled down helped fuel a recovery in bond markets.

Morgan Guaranty Trust Co., the nation's fifth largest, was the first to boost the rate from 19 1/2 to 20 percent, but by the end of the business day most other major banks had followed Morgan's lead.

The prime rate, the key business lending charge posted by banks, has risen from 17 percent in only a month, mainly because the Federal Reserve Board, the nation's central bank, has been trying to restrain credit growth by cutting back on the availability of funds in the banking system.When demand for funds stays high -- business loans have been growing -- a restriction in the growth of lendable funds usually causes interest rates to rise.

However, in the parlance of economists, the prime rate is a "lagging" rate, that is, one based on the costs banks faced in raising funds during the last few weeks. Usually the prime rate starts to rise some time after other interest rates begin their climb and starts to fall after other rates have peaked and begun their decline. Economists think that short-term interest rates -- those paid on investments that mature in less than a year (and sometimes in as little time as one day) -- will continue to rise until the Federal Reserve is convinced that it has control over the growth of the money supply and eases up on its strict monetary policy.

White House Deputy Press Secretary Larry Speakes repeated the common administration stand that its economic policies, if adopted by Congress, will help lower interest rates.

The Federal Reserve Board's policy making Open Market Committee met in Washington today to decide the course of monetary policy for the next several weeks. Minutes of today's meeting will not be available for a month.

The key indicator of Federal Reserve policy, the so-called federal funds rate, was stable today, trading in a narrow range around 18 1/2 percent.

Morse said that the rate on six month certificates of deposit, a major source of funds for banks, declined sharply today from nearly 18 percent to about 17 percent. But other key short-term rates, such as those paid on Treasury bills, showed virtually no change.

Thirty-year government bonds rose in price (bond prices rise when interest rates decline) by about $7.50 on each $1,000 of face value.