The Federal Reserve Board reported yesterday that industrial production skidded 2.1 percent last month, the most since the end of the 1974-75 recession and a further sign that the economy is continuing to slide.

The decline, which followed a 2 percent drop in April, marked the fourth month in a row that production levels have fallen. About half the latest dip was in autos and housing, but the rest was spread across the economy.

Meanwhile, interest rates continued to tumble in response to the weakening economy. Several large banks lowered their prime lending rates to 12 percent, from 13 percent. On Thursday, the Federal Reserve Board had lowered its key discount rate, the interest it charges on loans to member banks, by 1 percent.

The prime lending rate is the interest rate that banks charge their best corporate customers. Spurred by soaring inflation figures, the prime surged to a record 20 percent earlier this year before peaking in April.

The latest drop in the prime produced a mixed reaction in the Washington area. American Security National Bank dropped its prime to 12 1/2 percent, from 13 percent before. But Riggs National Bank remained unchanged at 13 percent.

Suburban Trust Company, the largest bank in Washington's Maryland suburbs, said it would lower its prime rate to 12 percent effective on Monday. The prime does not directly affect home mortgage interest rates.

Yesterday's statistics provided further confirmation that the recession is likely to be more severe than had been expected. The slump in 1974-75 was the worst since the Great Depression of the 1930s.

The nation's unemployment rate, only 6.2 percent in March, already has reached 7.8 percent of the work force, substantially above the 7.4 percent peak that the White House has forecast for yearend.

Lawrence Chimerine, economist at Chase Econometrics, Inc., noted that yesterday's figures showed the weakening had spread far beyond just autos and housing. "We've got quite a few months to go," he said, "before this is over."

However, officials confirmed yesterday the administration still is not considering either a tax cut or increased spending for public jobs programs. Some say a decision could come in a budget review next month.

The industrial production index measures the output of the nation's factories, mines and utilities and is a key indicator of the strength of the overall economy. The index often parallels changes in the unemployment rate.

Courtenay M. Slater, the Commerce Department's chief economist, pointed out in an article yesterday that Congress would have to enact a tax cut to ensure "an adequate pace of recovery" next year.

The figures on industrial production showed particularly sharp declines in output of autos and steel products and construction supplies. Auto assemblies plunged to an annual rate of 5.5 million units, down from 8 percent in April.

The overall index last month stood at 145.5 percent of its 1967 average, or 4.5 percent below the level of a year ago. Since peaking last January, the index has falled by 4.7 percent.

Production declines varied widely among various sectors of the economy. Output of consumer goods fell 6.1 percent last month, mainly as a result of the auto slump. Auto production now is 40 percent below a year ago. r

Production of construction supplies skidded 10.6 percent in May, while output of materials fell 5.2 percent. Production of business equipment continued to edge up, rising 0.4 percent in May.