Major banks raised their prime lending rates to 13 percent yesterday in the wake of an earlier 1-point rise in the Federal Reserve Board's discount rate. The prime was previously at 12 1/4 and 12 1/2 percent.

There has been a rapid succession of rises in the prime rate in the last few weeks.Bankers attribute these to a combination of increased loan demand, fears of renewed inflation and the market's expectation of a tightening in the Fed's money policy.

Yesterday's move was triggered by the discount rate increase to 11 percent, said spokesman for Chemical Bank and Citibank yesterday.

The monetary aggregates have recently been growing very rapidly, partly in reaction to their slump earlier this year. Yesterday the Fed reported further rises in both the narrower measures of the money supply in the week to September 17. The Fed also revised upwards the figures for the money supply in the previous week. The market had earlier been expecting a decline in the aggregates for the latest week, according to Chemical Bank economist and Senior Vice President, Frederick W. Deming.

A sharp increase in business loan demand in the nation's major banks was shown in the week to Sept. 17. Commercial and industrial loans rose by $1,365 million in the week, according to figures released through the New York Federal Reserve Bank. This compared with a rise of $747 million in the previous week. However, New York city banks saw a smaller increase, of $257 million, in their commercial and industrial loans n the latest week than the $348 million recorded the week before.

"Loan demand continues to be strong enough" to put pressure on interest rates, said Deming yesterday. He added that it was stronger than his other banks had expected earlier in the summer. "There is a slow, but certainly steady, upward movement in loan demand that is strong enough to make us want to be a little cautious," he said.

He pointed out that short-term interest rates had been rising before the Fed announced the increase in its discount rate and that they had surged further after the announcement.

Three-month certificates of deposit had been at 11.4 percent on Thursday morning. They rose to 11.9 percent by Thursday's close, after the Fed's announcement, and then climbed further to about 12.25 percent yesterday.

The Fed Funds rate, which used to be the key indicator of Fed money policy, averaged 10.8 percent in the week to Wednesday, but was up to 11.75 percent to 12 percent yesterday morning.

Continued high inflation, and the expectation that inflation will accelerate next year as the economy recovers further, has worked "hand in hand" with increased credit demand from business to push up interest rates, Deming said.

However, he still believes that rates will fall back in the next few months.

"Three months from today" they would be lower, he predicted.

Citibank economists are still looking for a fall in the prime before the end of the year, according to a spokesman for the bank. "But "how long they'll stick with that thesis is anyone's guess," the spokesman added.