NEW YORK (AP) _ Several of the nation's biggest banks today increased their prime lending rates to 11 percent from 10.5 percent, reflecting the continuing rise of interest rates on financial markets.

It was the first increase this year in the prime rate, which banks use as a benchmark for setting interest on a variety of consumer and corporate loans, and put the rate at its highest since it was 10.75 percent in late 1984.

The last increase, from 10 percent to 10.5 percent, was Nov. 28.

Chicago-based Continental Bank and Republic National Bank of New York were the first to boost their prime rates and soon were followed by Citibank, the nation's largest bank, and Chemical Bank.

Rates have been rising due partly to the Federal Reserve's tightening of credit in an attempt to curb inflation. The prime rate reflects a bank's costs of borrowing money, including interest it pays on savings accounts and certificates of deposit, and generally reflects more subtle increases in other interest rates.

The rate is watched closely because bankers use it as a basis for calculating interest on corporate loans and for determining many types of fixed and adjustable-rate consumer loans, such as home equity loans.

Republic said it increased its prime because of its rising cost of money. At Continental, Bank, the former Continental Illinois National Bank, officials said they wanted to bring the bank's rates in line with those on money markets.

Chemical Banking Corp., which owns Chemical Bank, is the nation's sixth- largest bank holding company.

Continental is owned by Continental Illinois Corp., the nation's 14th- largest holding company, while Republic's parent, Republic New York Corp., ranked 27th in terms of total assets held June 30, 1988.