Industrial production rose by 1 percent last month, according to figures released yesterday by the Federal Reserve Board. The report shows that the economy continued to be surprisingly strong during December, despite record-high interest rates.

But the December increase in the output of the nation's factories and mines was smaller than in preceding months, suggesting that growth may have begun to slow down slightly. Industry's production grew by an average of 1.7 percent a month for the three months prior to ydecember.

The recovery in output in the latter part of 1980 put it 7.3 percent higher in December than it had been in the deppths of recession in July. But the output rate was still 1.2 percent below the level of a year earlier.

For 1980 as a whole, the Fed estimates that output was 3 1/2 percent lower than in 1979. Many economists expect production to turn down again in the early months of this year, but the administration yesterday said it did not expect a recession during 1981.

A drop in auto production was largely responsible for slowing overal industrial production growth in December. High interest rates have hit the car market, and auto assembly dropped to an annual rate of 6.3 million units last month. This was 8 percent lowe than November's rate.

Consumer-durables production dropped by 1.3 percent in December because of the dragging effect of the auto figures. This followed an increase of 2 percent in November.

Nondurable-goods output rose by 0.9 percent, leaving an overall rise of 0.2 percent in consumer-goods production. There were "substantial gains in the output of residential utilities and consumer fuels," the Fed yboard said, which helped to keep up total consumer-goods production.

There was a rise of nearly 1 percent in the output of business equipment, about the same as in November and October. So far business still is projecting rising capital spending this year, despite the high cost of money.

Commerce Department Deputy Chief Economist William Cox noted that recent Commerce figures have shown relatively tight business inventories, while demand for some products and materials remains strong. Under those condtions, he said, "you don't suddenly have a recession setting in."

But he also commented that he would not be surprised if output growth slowed further in 1981.

Steel production continued to rebound last month. A post-strike surge in copper production and rsing output of energy materials helped push total production of materials up by 1.6 percent from November. A 0.9 percent increase in energy-materials production was due mainly to increased coal output and electric power generation, the Board said.

Output figures for previous months have been revised upwards slightly, the Board said. Recent revisions of other economic statistics have shown significantly faster growth in the economy in the second half of last year than first estimated.