Many of the nation's major banks boosted their prime lending rate to 17 percent today, following the lead of Continental Illinois National Bank, the nation's seventh biggest, which moved to 17 percent late Thursday.

But Citibank, New York's largest, announced this morning it would increase its prime rate -- the interest it charges its best corporate customers for a short-term loan -- to 16 3/4 percent.

The bank would not explain why it raised its prime rate less than most of its competitors other than to say it "was our own market judgment" that a 16 3/4 percent prime rate was called for now.

The prime rate at most major banks has risen from 15 1/2 percent to 17 percent in less than a week, mainly because of skyrocketing interest rates in the open market where banks raise most of the funds they lend to their customers. Analysts said the prime rate can be expected to rise again soon, although most do not see it hitting the record 20 percent banks posted in early April. The rate fell to 11 percent in July before resuming a climb in August.

Open-market interest rates continued to rise today, according to William Sullivan, vice president of the Bank of New York. Rates on certificates of deposit, the borrowing tool banks use to raise funds, rose between 20 and 30 basis points (a basis point is one one-hundredth of a percentage point) today.

Banks now must pay about 16.40 percent to borrow funds for three months, Sullivan said. A week ago banks had to pay investors about 15.15 percent.

Because of Federal Reserve Board rules, the real cost to banks of obtaining funds is higher than 17 percent, one of the reasons analysts expect another prime rate increase. Many banks today boosted the charge they levy on loans to brokers, usually an augur of increases in the prime rate.

The recent rise in short-term rates has been brought about in large part by Federal Reserve efforts to tighten monetary policy in an attempt to restrict the growth of the money supply and fight inflation.

The federal funds rate -- the interest banks pay each other for overnight loans of excess reserves -- traded as high as 18 percent today. That rate is sensitive to Federal Reserve actions in the open market. When the central bank moved to supply reserves to the banking systems, the rate on federal funds fell to about 17 1/4 percent, where it ended the day, according to Sullivan. Last Friday the federal funds rate was about 15 1/4 percent.

In another interest-rate development, the Federal Housing Administration and the Veterans Administration raised to 13 1/2 percent from 13 percent the maximum interest rate that lenders can charge for government-backed home mortgages.

The two agencies said the higher rates better reflect conditions in the mortgage market. However, conventional mortgages, when they are available, are higher than 14 percent in most parts of the country and 15 percent or more in others.