Several of the nation's largest banks yesterday raised their prime lending rates - the interest they charge their most creditworthy corporate customers - a reaction both to rising short-term interest rates and heightened loan demand.

The move, which pushed the prime rate to 7.75 per cent, up from 7.50 per cent before, was begun in mid-morning by Citibank, the nation's second largest bank. By late afternoon, more than a half dozen other large banks had followed suit.

Analysts said the shift reflected two factors:

The recent sharp rise in short-term interest rates - such as those of three month Treasury bills and the federal funds rate - which affect the prices banks pay for money. The federal funds rate is the interest charged on overnight loans to banks.

A new increase in business loan demand. The volume of business loans nationally soared by $505 million last week, heightening what has been a steady rise over the past few months. This week, loan demand jumped $480 million in New York alone.

The move came as, sepately, the Federal Reserve Board confirmed what already had been apparent in the nation's money markets - that its key Open Market Committee embarked on a significant credit-tightening last month to offset an earlier expansion.

The board said the panel voted at its Sept. 20 meeting to try to hold the federal funds rate to between 6 and 6-50 per cent, down from the previous target of 5.25 to 6.25 per cent that had prevailed since last August. The panel's decision are made public within 45 days.

The increase in the prime rate was not expected to have an immediate impact on most long-term interest rates, including home-mortgage rates, which are based on other market indicators. However, it could affect interest rates on consumer loans.

The rise was the sixth so far this year. At this time 13 months ago, the prime rate was 6.78 per cent.

Shifts in the prime rate by Citibank have become a key mover in the industry in recent years. The bank has hinged its prime to a special formula designed to peg the rate automatically 1.25 percentage-points above the interest rate for three-month commercial paper.

That rate to 6.50 per cent last week. Commercial paper is short-term notes issued by businesses to public lenders. Generally, they are unsecured.

In the announcement on the Open Market Committee decision, the report that while the tightening was intended only to offset earlier monetary expansion, the step was viewed with apprehension by some members of the panel, who fear it might damage the economy.

Although some on the panel believe the recovery is still on track, the records show some members have expressed concern about the outlook for economic growth. The Federal Reserve is engaged in a dispute with the administration over monetary policy.

The banks that followed Citibank in raising their prime rates yesterday included three St. Louis Banks - the First National Bank of St. Louis, Boatmen's National Bank and Mercantile Trust Co. - the First National Bank of Boston and First Wisconsin National Bank of Milwaukee.

Industry analysts said the rise was expected to become firm nationwide on Tuesday, when banks re-open after the Veterans' Day holiday.