The Federal Reserve Board responded to a barrage of unsettling economic news yesterday -- including a sharp surge in the weekly money supply figures -- by increasing a key interest rate a full percentage point, to a record 13 percent.

The Fed's intention in raising its discount rate, the interest rate it charges on loans to banks belonging to the Federal Reserve system, was seen by most analysts as a signal to reassure uneasy financial markets the central bank will not relent in its fight against inflation.

Producer prices for finished goods rose 1.6 percent in January, the worst performance for the index in five years. Industrial production climbed 0.3 ercent for the same month, not a large increase but a further sign, along with a strong 2.3 percent jump in retail sales, that the economy is not dropping into recession as expected.

Couple that news with a $3.7 billion surge in the money supply measure known as M1-A, which includes currency in circulation and demand deposits at commercial banks, and some new assurances were in order, analysts said.

In fact, several of the regional Federal Reserve Banks had been pressing the board for some time to raise the discount rate, sources said. Federal Reserve staff analyses were predicting a significant quickening in the rate of increase in the monetary aggregate this month. And there seemed to be a growing belief in business and financial circles that any recession in 1980 would be brief and do little to halt inflation.

The discount rate increase, one analyst said, "does not represent a change in Federal Reserve policy, but rather a recognition by the Fed that more may be needed in the way of higher interest rates" to reach its monetary growth targets. "They had to remind everyone that they have those targets and intend to meet them."

For months now, Fed Chairman Paul Volcker has been telling Congress and the public the Fed will stick it out. "I can assure you we are committed to maintaining over time the discipline that is necessary to moderate . . . excessive growth in the supply of money and credit," Volcker said in a recent speech.

Volcker will disclose the Fed's new money growth targets for 1980 in testimony Tuesday before the House Banking Committee.

Since the Federal Reserve is no longer seeking to influence the money supply by controlling certain market interest rates as it did prior to last October, analysts were uncertain exactly what effect raising the discount rate would have on other interest rates.

Following the Fed's morning announcement, however, Wells Fargo Bank of San Francisco raised its prime lending rate to 15 1/2 percent from the 15 1/4 percent level generally prevailing at major banks.

In the announcement, the Fed said it "has been particularly concerned that recent economic developments, including the large increase in the price of imported oil, are adding to inflationary pressures and may lead to further destabilizing pricing decisions. These developments underscore the need to take such measures as may be required to maintain firm control over growth of money and credit."

Some analysts, such as Salomon Brothers' Henry Kaufman, noted that interest rates had been firming before the Fed acted. Kaufman predicted the prime rate would soon reach 15 3/4 percent.