In a further response to the fast-worsening recession, several of the nation's largest banks dropped their prime lending rates again yesterday, this time to 16 1/2 percent, from 17 1/2 percent.

The drop, the latest in a series of declines since the prime peaked at 20 percent a few weeks ago, was led by Morgan Guaranty Trust Company of New York. The prime is the interest rate banks charge their most credit-worthy customers.

The percentage-point decline reflects a reduction in banks' own borrowing costs and a continued falloff in business loan demand in the face of deteriorating economic conditions across the nation.

Separately, the Commerce Department reported that business inventories rose 0.6 percent, or $2.55 billion, in March, following an 0.8 percent, $3.55 billion increase the previous month.

The closely watched inventory-to-sales ratio also edged up, showing businesses now have sufficient stocks on hand to cover 1.42 months' sales, compared to 1.40 months in February. Analysts say inventories are not yet excessive.

Meanwhile, the White House denied that officials are studying a tax cut for 1981, reiterating that the administration will reassess the situation "somewhere down the road," but only after the budget is balanced.

Presidential press secretary Jody Powell also renewed President Carter's insistence that any new tax cut be "carefully targeted" to enhance productivity and investment, but he mentioned no specific plan.

Congressional conservatives have rallied behind a bill by Reps. James R. Jones (D-Okla.) and Barber B. Conable (R-N.Y.) to provide faster depreciation writeoffs for business, but so far the lawmakers seem content to put off any action.

Any another development, Anthony M. Solomon, president of the New York Federal Reserve Bank, proposed a four-point anti-inflation program calling for reduced government borrowing, a cutback in oil imports tight money and stiffer wage-price rules.

Solomon also urged enactment of new incentives for saving and investment and said officials should weigh tradeoffs more seriously in setting regulations for health, safety and environmental enforcement.

The inventory figures showed stock-building in March at $437.62 billion. Retailers' inventories rose 0.2 percent, to $108.92 billion. Overall business sales declined 0.9 percent, or $2.92 billion, to $307.57 billion.

The department said manufacturers' inventories rose 1.4 percent in March to $238.1 billion, while wholesalers' stocks fell 1 percent to $90.6 billion. All figures were adpusted to compensate for seasonal patterns.