Most of the nation's major banks dropped their prime lending rates to 19 percent from 19 1/2 percent today, following the lead of Continental Illinois National Bank, Chicago's biggest, which dropped its key lending rate Friday.

The prime rate -- normally considered the best rate a top corporation can get for a loan of three months to a year--is expected to fall farther in the next week or two because of the recent decline in short-term interest rates in the open market, where banks raise much of the funds they in turn lend to business customers.

For example, according to Nicholas Marrone of the Bank of New York, the rate on three-month certificates of deposit was 16.05 percent today. Several months ago the rate was about 18 1/2 percent.

At 19 percent, however, interest rates remain at near-record levels. Rates have come down in recent weeks mainly because of a weakening economy, although some analysts think the Federal Reserve Board, the nation's central bank, has relaxed slightly its tight monetary grip. The Fed has come under mild pressure from the Reagan administration, which fears continued stringent monetary policy will trigger a severe recession.