The Federal Reserve Board, alarmed by new figures showing worsening inflation, announced yesterday another 1 percentage point increase in interest rates and warned it will tighten credit still further if this action does not work.

By unanimous vote, the board raised its so-called discount rate -- the interest it charges on loans to member banks -- to a record 13 percent from 12 percent. It also vowed to take "other measures as may be required" if the new inflation rate persists.

The Fed's action, the most important piece of credit-tightening in four months, came as the Labor Department reported a 1.6 percent increase last month in prices charged by producers, the largest monthly increase in five years.

The increase came almost entirely in energy and in gold and silver prices. It nevertheless pointed to sharp price increases at the retail level in coming months. Producer prices were 13 percent above their levels a year ago.

The Fed's vote to raise interest rates was intended as a signal that the board will hold firm on inflation even in the face of a predicted recession.

There had been a growing sense on Wall Street that the Fed was too easy in supplying funds to banks. Some analysts complained that was contributing to inflationary pyschology.

The new action had an immediate impact. Shortly after the Fed's announcement, the Wells Fargo Bank of San Francisco raised its prime interest rate charged to big corporations to 15.5 percent from 15.25 percent.

The stock market also reacted sharply, with the Dow Jones industrial average off 8.79 points at the close, after plunging further but then recovering. The dollar gained worldwide, while gold prices fell.

The Carter administration offered no comment on the Fed's announcement. The president is trying to maintain a restrictive budget policy in hopes of winding inflation down while averting a deep recession.

The increase in producer prices came despite a 0.8 percent drop in wholesale food prices in January. Prices of other consumer finished goods soared 2.4 percent, compared to a 1.1 percent increase in December.

Analysts said about 0.4 percentage points of the 1.6 percent rise in producer prices stemmed from soaring gold and silver prices, which skewed the index in January, and 0.4 to 0.5 percentage points came from higher crude oil prices.

Both government and private economists are substantially more pessimistic about the inflation outlook than they were even a few weeks ago. Most now expect retail prices to rise by 10 percent or more during 1980.

In another development, the Fed announced that the nation's industrial output rose only 0.3 percent during January, continuing the sluggishness that began last October.

The production increase came despite another sharp drop in auto output, which fell 2.2 percent over the month. Other sectors of the economy were mixed. Industrial production has remained virtually level over the past three months.

The 1.6 percent rise in producer prices came among products that were ready to be shipped to retailers. The index for the preceding stage of production showed prices up 2.8 percent, following a 1.1 percent increase in December.

The producer price index last month stood at 232.1 percent of its 1967 average. That means it took 232.10 to buy the same goods from producers that cost $100 just 13 years ago.

In announcing its move, 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.

It said "these developments underscore the need to take such measures as may be required to maintain firm control over growth of money and credit."

Yesterday's action marked the latest in a series of tough credit-tightening moves by the Fed, and the second under conservative chairman Paul A. Volcker, who took over last August.

The increases began as part of a November 1978 effort to stem a slide in the value of the dollar, and intensified in later months to bring on the highest interest rates in history.

The last major action, which also involved a 1 point increase in the discount rate, rocked the financial markets and brought predictions of a serious recession, but Wall Street -- and the economy -- survived without injury.

Since then, the Fed has succeeded in bringing the growth of the nation's money supply under control, but in recent weeks the markets once again have raised fears that the Fed was too soft on inflation.

In another action yesterday, the Fed reported that American factories operated at 84.3 percent of their capacity in January, unchanged from December's levels. CAPTION: Picture, The Price Of Inflation -- Sen. William V. Roth Jr. (R-Del.) demonstrates the effect of inflation outside the Capitol yesterday, showing that today's $6,000 car will cost more than $20,000 in 1990 if the inflation rate continues, and a person who paid $3,391 in federal income tax in 1980 will pay nearly $22,000 in federal taxes in 1990.