The nation's major banks posted another sharp increase in their prime lending rates yesterday, boosting them to 16 1/4 percent, from 15-1/2 percent before. Interest rates in the money markets climbed steeply as well.

Both developments followed the Federal Reserve Board's decision late Friday to raise its discount rate -- the interest it charges on loans to member banks -- from 11 percent to 12 percent. The Fed also tacked on a 2 percentage-point surcharge for big banks that were heavy borrowers at the Fed's discount window.

The surcharge is retroactive to Oct. 2, so some banks presumably found they had to pay 14 percent in interest for funds they borrowed originally at 11 percent from the central bank. The Fed also reported yesterday a big surge in business loan demand during the first week in November.

Chase Manhattan Bank, New York's third largest, led the way today as it has so many times during recent mmonths, both when the prime lending rate was declining sharply last spring, and when it began its most recent climb in August. The prime rate hit 20 percent last April, and then fell to 11 percent by July.

Chase announced the increase to 16 1/4 percent shortly after 10 a.m., and nearly all major banks had followed by noon. The prime is the interest rate banks charge their best corporate customers for short-term loans. Locally, the Riggs National Bank, largest in the Washington area, announced a similar increase, effective this morning.

A spokesman for Chase blamed rising market interest rates for the latest increase in the prime, and argued the increase would not even cover the bank's own cost of obtaining funds.

The spokesman said Friday's increase in the discount rate increase was not that important a factor in Chase's decision. Rather, he aserted, it was the rise in open mmarket rates that forced Chase's decision.

Most major banks issue short-term securities in the open market -- usually large-sized certificates of deposit -- to obtain funds that they can later lend to their business customers. Rates in the open market had risen during the last few weeks and today, following the prime rate increases and the Fed's discount rate hike, those rates skyrocketed.

William Sullivan, vice-president of the Bank of New York, said that some rates increased by 75 to 100 basis points (three-quarters of a percentage-point to a full percentage-point) today alone.

As a result, for example, banks selling 3-month certificates of deposit late Friday had to pay investors about 15.15 percent. Today, the rates on those certificates rose to 16 percent.

Federal funds -- excess reserves that banks sell each other for overnight use -- cost banks as much as 18 percent or 19 percent today, compared with about 15 1/4 percent Friday.

The Federal Reserve took some steps today to supply reserves to the banking system, but the action had little impact on the rise in interest rates -- particularly the federal funds rate, which is very sensitive to Federal Reserve monetary policy maneuvers.