In a further dramatic sign of recession, the government reported yesterday that housing starts, choked off by soaring mortgage rates, fell 21.8 percent in March, the most they have dropped in any month in 20 years.

The housing report came as several of the nation's largest banks, reacting to a recent falloff in demand for loans, reduced the prime lending rates charged major corporations to 19 3/4 percent from the record 20 percent.

That was regarded by analysts as another indication that interest rates have finally peaked, and will probably edge down slowly over the next few weeks.

In other recessionary news, General Motors Corp. announced it will lay off another 12,000 employes at seven assembly plants across the nation over the next few weeks as part of an industry-wide effort to stave off losses.

Meanwhile, President Carter met with a group of housing industry leaders in preparation for possible announcement today of new government actions to ease the burden of high interest rates on construction.

The White House is expected to liberalize the "Section 235" home-ownership assistance program to include middle-income buyers purchasing houses costing up to $60,000. The measure is being regarded as a token step.

The sharp March drop in housing starts was another in a series of recent statistics indicating that the long-predicted recession finally has arrived. The slump was averted last year because consumers kept on spending.

The Federal Reserve Board has been pushing up interest rates for months to combat inflation. In March, with inflation still running almost unchecked at 18 to 20 percent, Carter ordered further credit restrictions, and proposed new spending cuts as well to balance the budget.

If the administration now acts to alleviate the burdens on the housing industry, it will be acting partly counter to these measures. Officials describe the contemplated actions as intended to "even out" the effect of tight money and high interest rates.

News of the weakening economy, and the prospect that the slump might help slow inflation, sent the bond market into a major rally yesterday. It was the near-collapse of the bond market in February that made Carter shift policy then.

However, yesterday's drop in the prime rate pushed the dollar down sharply on the foreign exchange markets, as traders rushed to beat a slide some believe will result as interest rates here move closer to those overseas.

Treasury Secretary G. William Miller told Congress it was premature to say the bond market had regained its former strength, but he said "the healing process is under way," and predicted the markets soon would be restored.

The layoffs by General Motors were the latest in a series of plant-closings and cutbacks by the Big Three automakers, whose sales have been slumping as Americans rush to buy smaller -- often foreign-produced -- cars.

One Tuesday, Ford Motor Co. announced it would lay off some 15,000 employes and close its entire Mahwah, N.J., plant. Union leaders say more than 250,000 auto workers are on temporary or indefinite layoff.

Yesterday, United Auto Workers union president Douglas A. Fraser said the UAW will send 800 local officers to Washington May 8 for a day of lobbying in behalf of new restrictions on auto imports.

Charging that American autoworkers are in "a depression," Fraser urged Carter to require that Japanese automakers establish more U.S. plants if they want to continue to sell large numbers of cars here.

Meanwhile, in yet another indication of the worsening slump, the Federal Reserve Board reported that the nation's factories operated at only 83 percent of capacity in March, the lowest level in two years.

The Commerce Department said housing starts nationwide plunged to an annual rate of 1.041 million units, 42.2 percent below a year ago and the lowest since March 1975, near the end of the 1974-75 recession.

The number of new building permits taken out in March also plummeted, indicating the housing slump most likely will worsen.

Permits fell 21.2 percent in February to a level 35.1 percent below a year ago. Starts of single-family homes fell 23.2 percent in March to an annual rate of 606,000, down 52.5 percent from a year ago.

Analysts were divided over how much further the housing industry would slump before the downturn ended.

William A. Cox, the Commerce Department's deputy chief economist, said yesterday he thought "the bulk of the decline" had passed.

However, Michael Sumichrast, economist for the National Association of Home Builders, predicted starts ultimately could plunge to an annual rate of 800,000 units, marking the worst slump since World War II. He said the March figures reflect only a portion "of what's going in the field," where he said soaring interest rates have brought home sales almost to a halt.

However, Sharon Skeiber, economist for the Federal Home-Loan Mortgage Corp., said some of the plunge stemmed from efforts by builders to bring their inventories into line with sales levels.

Yesterday's reduction in the prime rate began with Chase Manhattan Bank and quickly spread to medium-sized and large banks in Pittsburgh and several other cities. The prime is the rate charged to the most credit-worthy firms.