Manufacturers Hanover Trust Co. and Chemical Bank, the nation's fourth and seventh biggest banks, yesterday cut their prime lending rate from 16 percent to 15 1/2 percent, the second reduction in the key business interest rate in as many weeks.

Further cuts in the prime rate are expected in the next few weeks as banks adjust their lending charges to reflect the dramatic drop in their cost of funds since the beginning of July.

The prime rate is the interest rate banks charge their best corporate customers for short-term loans and the rate on which most other short-term business borrowing is based.

Bank borrowing charges are likely to remain high by historical standards, however, and will continue to be a barrier to economic recovery and a threat to the financial health of many companies, analysts say.

Short-term interest rates in the so-called open market--where banks "buy" money from companies with spare cash and from money-market mutual funds--have fallen sharply, analysts said, because of an easing in the Federal Reserve's monetary policy.

Banks, for example, had to pay an average annual interest rate of 15.05 percent in late June to sell $1 million certificates of deposit to large investors. Yesterday they could sell that same type of deposit for 11.25 percent, according to William Sullivan, vice president of the Bank of New York.

The Federal Reserve, the nation's central bank, apparently has felt comfortable supplying more funds to the banking system because the money supply, the prime target of Federal Reserve policy, has slowed its growth to within a range it considers desirable.

Ironically, on the same day two big banks cut their prime lending rate as a result of the month-long decline in their interest costs, open-market interest rates rose--both in the government securities market and the private money markets.

Bank of New York's Sullivan said the interest rate rise reflected both fears of the huge Treasury refinancing scheduled to be announced Wednesday as well as a smaller-than-hoped-for decline in the money supply reported last Friday. "This reduces the Fed's running room," Sullivan said.

The Treasury is expected Wednesday to borrow at least $10 billion and perhaps as much as $12 billion to finance the growing budget deficit. In anticipation of that borrowing, interest rates on government securities rose yesterday and prices fell. Prices of longer-term Treaury bonds were down as much as $15 on a face value of $1,000 and $10 on issues that mature between four and 10 years.

Nevertheless, unless an unexpected development should occur, interest rates are expected to remain so far below the current prime rate that a cut to 15 percent would be in order as soon as next week, Sullivan said.

Beyond that, however, banks will be reluctant to lower their prime rates too quickly. Bank profitability has been hurt in recent years when interest rates moved upward but banks could not raise the prime rate fast enough to cover their rising costs for funds. Now they want to recover some of those profits as rates come down.

At the same time, said one major banker, the financial institutions know that continued high rates make business failures more likely. As a result, banks are caught between one desire to recoup lost profits and another to keep their customers healthy.

As a result, most analysts expect regular small cuts in the prime lending for the next few weeks unless interest rates surge again.